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2
.travis.yml
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@ -177,7 +177,7 @@ matrix:
sources:
- ubuntu-toolchain-r-test
- llvm-toolchain-precise-3.7
# Fails to compile std lib headers (toolset issue):
#- os: linux
# env: TOOLSET=clang COMPILER=clang++-3.8 CXXSTD=03,11,14,1z

10
README.md
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@ -18,24 +18,24 @@ There is no mailing-list specific to Boost Graph, although you can use the gener
## Development ##
Clone the whole boost project, which includes the individual Boost projects as submodules ([see boost+git doc](https://github.com/boostorg/boost/wiki/Getting-Started)):
Clone the whole boost project, which includes the individual Boost projects as submodules ([see boost+git doc](https://github.com/boostorg/boost/wiki/Getting-Started)):
git clone https://github.com/boostorg/boost
cd boost
git submodule update --init
The Boost Graph Library is located in `libs/graph/`.
The Boost Graph Library is located in `libs/graph/`.
Boost Graph Library is mostly made of headers but also contains some compiled components. Here are the build commands:
./bootstrap.sh <- compile b2
./bootstrap.sh <- compile b2
./b2 headers <- just installs headers
./b2 <- build compiled components
**Note:** The Boost Graph Library cannot currently be built outside of Boost itself.
### Running tests ###
First, make sure you are in `libs/graph/test`.
First, make sure you are in `libs/graph/test`.
You can either run all the 300+ tests listed in `Jamfile.v2` or run a single test:
../../../b2 <- run all tests

12
doc/AStarHeuristic.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) 2004 Kris Beevers
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: AStarHeuristic</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -135,4 +135,4 @@ HREF="mailto:beevek@cs.rpi.edu">beevek@cs.rpi.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/AStarVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) 2004 Kris Beevers
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: AStarVisitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -210,4 +210,4 @@ HREF="mailto:beevek@cs.rpi.edu">beevek@cs.rpi.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

58
doc/AddEdgeVisitor.html
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@ -1,21 +1,21 @@
<html>
<head>
<!-- Copyright 2007 Aaron Windsor
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<title>AddEdgeVisitor Concept</title>
</head>
<body alink="#ff0000"
bgcolor="#ffffff"
link="#0000ee"
text="#000000"
vlink="#551a8b">
<body alink="#ff0000"
bgcolor="#ffffff"
link="#0000ee"
text="#000000"
vlink="#551a8b">
<img src="../../../boost.png" alt="C++ Boost" height="86" width="277">
<img src="../../../boost.png" alt="C++ Boost" height="86" width="277">
<br clear="">
@ -23,7 +23,7 @@
The AddEdgeVisitor concept exists to allow for some indirection in algorithms
that modify graphs by adding edges. In such algorithms, it may be convenient
to perform additional operations (such as updating an edge index map) at
to perform additional operations (such as updating an edge index map) at
points in the algorithm where an edge addition occurs. Replacing calls to
to <tt>add_edge</tt> with calls to <tt>AddEdgeVisitor::visit_vertex_pair</tt>
allows for such operations to be defined independently from the algorithm.
@ -38,8 +38,8 @@ allows for such operations to be defined independently from the algorithm.
<td> is a type that models the AddEdgeVisitor concept </td>
</tr>
<tr>
<td> <tt>vis</tt> </td>
<tr>
<td> <tt>vis</tt> </td>
<td> is an object of type Visitor </td>
</tr>
@ -48,15 +48,15 @@ allows for such operations to be defined independently from the algorithm.
<td> is the type of a graph </td>
</tr>
<tr>
<td> <tt>u,v</tt> </td>
<tr>
<td> <tt>u,v</tt> </td>
<td> are objects of type <tt>graph_traits&lt;Graph&gt;::vertex_descriptor</tt>
</td>
</tr>
<tr>
<td> <tt>e</tt> </td>
<td> is an object of type <tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>
<tr>
<td> <tt>e</tt> </td>
<td> is an object of type <tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>
</td>
</tr>
@ -66,7 +66,7 @@ allows for such operations to be defined independently from the algorithm.
</td>
</tr><tr>
<td>
<td>
</td></tr></tbody></table>
@ -84,7 +84,7 @@ None
<tbody><tr><th>Name</th><th>Expression</th><th>Return Type</th>
<th>Description</th>
</tr><tr>
</tr><tr>
<td> Add an Edge </td>
<td> <tt>vis.visit_vertex_pair(u, v, g)</tt> </td>
<td> <tt>void</tt></td>
@ -96,26 +96,26 @@ None
</p><h3>Models</h3>
Two models of this concept are defined in the file
Two models of this concept are defined in the file
<a href="../../../boost/graph/planar_detail/add_edge_visitors.hpp">
<tt>add_edge_visitors.hpp</tt></a>:
<ul>
<li><tt>default_add_edge_visitor</tt>: The constructor of this class takes
no arguments.<tt>visit_vertex_pair(u, v, g)</tt> is just a dispatch to
<tt>add_edge(u, v, g)</tt>.
<tt>add_edge(u, v, g)</tt>.
<li><tt>edge_index_update_visitor</tt>: The constructor of this class takes
two arguments: the first, an EdgeIndexMap,
is a <a href="../../property_map/doc/ReadWritePropertyMap.html">
ReadWritePropertyMap</a> that maps each edge in the associated graph
<tt>g</tt> to a distinct integer in the range <tt>[0, num_edges(g))</tt>.
The second argument is the number of edges in the underlying graph, which
ReadWritePropertyMap</a> that maps each edge in the associated graph
<tt>g</tt> to a distinct integer in the range <tt>[0, num_edges(g))</tt>.
The second argument is the number of edges in the underlying graph, which
serves as the "next available index" counter within the visitor.
For example, in the case the graph used has an initialized interior
edge index, the <tt>edge_index_update_visitor</tt> constructor should be
called with <tt>get(edge_index, g)</tt> as the edge index and
<tt>num_edges(g)</tt> as the next available index. When
<tt>visit_vertex_pair(u, v, g)</tt> is called, the
For example, in the case the graph used has an initialized interior
edge index, the <tt>edge_index_update_visitor</tt> constructor should be
called with <tt>get(edge_index, g)</tt> as the edge index and
<tt>num_edges(g)</tt> as the next available index. When
<tt>visit_vertex_pair(u, v, g)</tt> is called, the
<tt>edge_index_update_visitor</tt> will add the edge <i>(u,v)</i> to the graph
and update the edge index for the newly created edge.
</ul>
@ -125,6 +125,6 @@ and update the edge index for the newly created edge.
<br>
</p><hr>
Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
aaron.windsor@gmail.com</a>)
</body></html>

12
doc/AdjacencyGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>AdjacencyGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -164,4 +164,4 @@ experience with graph algorithm implementations.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/AdjacencyMatrix.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>AdjacencyMatrix</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -100,4 +100,4 @@ The <TT>edge()</TT> function must return in constant time.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/BFSVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: BFSVisitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -142,7 +142,7 @@ edges for undirected graphs.
<td>
This is invoked on the subset of non-tree edges whose target vertex is
colored gray at the time of examination. The color gray indicates
that the vertex is currently in the queue.
that the vertex is currently in the queue.
</td>
</tr>
@ -217,4 +217,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

16
doc/BasicMatrix.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>BasicMatrix</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -78,11 +78,11 @@ Element access is constant time.
void constraints() {
V&amp; elt = A[i][j];
const_constraints(A);
ignore_unused_variable_warning(elt);
ignore_unused_variable_warning(elt);
}
void const_constraints(const M&amp; A) {
const V&amp; elt = A[i][j];
ignore_unused_variable_warning(elt);
ignore_unused_variable_warning(elt);
}
M A;
I i, j;
@ -100,4 +100,4 @@ HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/BellmanFordVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Bellman Ford Visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -181,4 +181,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/BidirectionalGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Bidirectional</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -177,4 +177,4 @@ undirected graphs).
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

16
doc/Buffer.html
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@ -1,7 +1,7 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
@ -9,10 +9,10 @@
<Head>
<Title>Buffer</Title>
</HEAD>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -43,7 +43,7 @@ For a type to model the Buffer concept it must have the following members.
<tr> <td><b>Member</b></td> <td><b>Description</b></td> </tr>
<tr> <td> <tt>value_type</tt> </td>
<tr> <td> <tt>value_type</tt> </td>
<td> The type of object stored in the Buffer. The value type
must be <A href="http://www.boost.org/sgi/stl/Assignable.html">Assignable</a>.</td>
</tr>
@ -70,7 +70,7 @@ For a type to model the Buffer concept it must have the following members.
</tr>
<tr> <td> <tt>const T& top() const</tt> </td>
<td> Returns a const reference to some object in the Buffer.
<td> Returns a const reference to some object in the Buffer.
Precondition: <tt>empty()</tt> is <tt>false</tt>.</td>
</tr>
@ -114,5 +114,5 @@ most linear time complexity in the size of the Generalized Queue.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/ColorValue.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: ColorValue Concept</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -105,4 +105,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

30
doc/DFSVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>DFS Visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -150,15 +150,15 @@ undirected graph this method is never called.
</tr>
<tr>
<td>Finish Edge</td>
<td><tt>vis.finish_edge(e, g)</tt></td>
<td><tt>void</tt></td>
<td>
This is invoked on each non-tree edge as well as on each tree edge after
<tt>finish_vertex</tt> has been called on its target vertex.</td>
</tr>
<tr>
<td>Finish Edge</td>
<td><tt>vis.finish_edge(e, g)</tt></td>
<td><tt>void</tt></td>
<td>
This is invoked on each non-tree edge as well as on each tree edge after
<tt>finish_vertex</tt> has been called on its target vertex.</td>
</tr>
<tr>
<td>Finish Vertex</td>
<td><tt>vis.finish_vertex(u, g)</tt></td>
<td><tt>void</tt></td>
@ -218,4 +218,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/DijkstraVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Dijkstra Visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -219,4 +219,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

16
doc/EdgeListGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>EdgeListGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -109,7 +109,7 @@ Return type: <TT>vertex_descriptor</TT>
<tr>
<TD><TT>target(e, g)</TT></TD>
<TD>
Returns the vertex descriptor for
Returns the vertex descriptor for
<i>v</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
Return type: <TT>vertex_descriptor</TT>
</TD>
@ -143,7 +143,7 @@ must all return in constant time.
template &lt;class G&gt;
struct EdgeListGraphConcept
{
typedef typename boost::graph_traits&lt;G&gt;::edge_iterator
typedef typename boost::graph_traits&lt;G&gt;::edge_iterator
edge_iterator;
void constraints() {
BOOST_CONCEPT_ASSERT(( GraphConcept&lt;G&gt; ));
@ -181,4 +181,4 @@ must all return in constant time.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/EdgeMutableGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Edge Mutable Graph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -35,7 +35,7 @@ No additional associated types.
<ul>
<li><a name="sec:add_edge"><TT>add_edge(u, v, g)</TT></a>
<li><a name="sec:add_edge"><TT>add_edge(u, v, g)</TT></a>
<b>returns</b> <TT>std::pair&lt;edge_descriptor,&nbsp;bool&gt;</TT>
<br><br>
@ -105,4 +105,4 @@ UNDER CONSTRUCTION
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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doc/EventVisitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: EventVisitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -158,4 +158,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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doc/EventVisitorList.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: EventVisitorList</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -124,4 +124,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

16
doc/Graph.html
View File

@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Graph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -85,8 +85,8 @@ are <TT>allow_parallel_edge_tag</TT> and <TT>disallow_parallel_edge_tag</TT>.
<td><pre>boost::graph_traits&lt;G&gt;::traversal_category</pre>
This describes the ways in which the vertices and edges of the
graph can be visited. The choices are <TT>incidence_graph_tag</TT>,
<TT>adjacency_graph_tag</TT>, <TT>bidirectional_graph_tag</TT>,
<TT>vertex_list_graph_tag</TT>, <TT>edge_list_graph_tag</TT>, and
<TT>adjacency_graph_tag</TT>, <TT>bidirectional_graph_tag</TT>,
<TT>vertex_list_graph_tag</TT>, <TT>edge_list_graph_tag</TT>, and
<TT>adjacency_matrix_tag</TT>.
</td>
</tr>
@ -145,4 +145,4 @@ any vertex of graph object which type is <tt>G</tt>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/IncidenceGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>IncidenceGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -199,4 +199,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

18
doc/IteratorConstructibleGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>IteratorConstructibleGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -51,13 +51,13 @@ and can therefore be used to construct a graph.
typedef ... IteratorConstructibleGraph;
typedef boost::graph_traits<IteratorConstructibleGraph> Traits;
typedef std::pair<Traits::vertices_size_type,
typedef std::pair<Traits::vertices_size_type,
Traits::vertices_size_type> Edge;
Edge edge_array[] =
{ Edge(0,1), Edge(0,2), Edge(0,3), Edge(0,4), Edge(0,5),
Edge(1, 2), Edge(1,5), Edge(1,3),
Edge(2, 4), Edge(2,5),
Edge(3, 2),
Edge(3, 2),
Edge(4, 3), Edge(4,1),
Edge(5, 4) };
Edge* first = edge_array,
@ -65,7 +65,7 @@ and can therefore be used to construct a graph.
IteratorConstructibleGraph G1(first, last);
// do something with G1 ...
Traits::vertices_size_type size_V = 6;
Traits::edges_size_type size_E = sizeof(edge_array)/sizeof(Edge);
IteratorConstructibleGraph G2(first, last, size_V, size_E);
@ -158,4 +158,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

10
doc/KeyedUpdatableQueue.html
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@ -9,7 +9,7 @@
<head>
<title>KeyedUpdatableQueue</title>
</head>
<body>
<body>
<img src="../../../boost.png" alt="C++ Boost">
<h2><a name="concept:KeyedUpdatableQueue">KeyedUpdatableQueue</a></h2>
@ -28,7 +28,7 @@ values are mapped via a read/write key map.
<h3>Members</h3>
For a type to model the KeyedUpdatableQueue concept it must have the following members
For a type to model the KeyedUpdatableQueue concept it must have the following members
in addition to the members that are required of types that model <a href="./UpdatableQueue.html">UpdatableQueue</a>:
<p>
@ -61,17 +61,17 @@ in addition to the members that are required of types that model <a href="./Upda
{
typedef typename Q::key_type key_type;
typedef typename Q::key_map key_map;
void constraints() {
BOOST_CONCEPT_ASSERT(( UpdatableQueue&lt;Q&gt; ));
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMap&lt; key_map, typename Buffer&lt;Q&gt;::value_type &gt; ));
}
void const_constraints(const Q&amp; cq) {
km = cq.keys();
k = get(km, g_ct);
}
static const typename Buffer&lt;Q&gt;::value_type g_ct;
key_type k;
key_map km;

2
doc/Makefile
View File

@ -41,7 +41,7 @@ RESULT = pdf
epstopdf $*.eps
.dot.eps:
dot -Tps -o $*.eps $*.dot
dot -Tps -o $*.eps $*.dot
.w.tex: /afs/nd.edu/user11/jsiek/.jweb
jweb -np $*.w

12
doc/Monoid.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Monoid</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -119,4 +119,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/MutableGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>MutableGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -59,7 +59,7 @@ edges and vertices.
<TD><tt>p</tt></TD>
<TD>is an object of a type that models <a
href="http://www.boost.org/sgi/stl/Predicate.html">Predicate</a>
and whose argument type matches the <tt>edge_descriptor</tt> type.
and whose argument type matches the <tt>edge_descriptor</tt> type.
</TR>
</table>
@ -296,4 +296,4 @@ is no longer a valid vertex descriptor.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/MutablePropertyGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>MutablePropertyGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -147,4 +147,4 @@ Return type: <TT>vertex_descriptor</TT>
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

68
doc/PlanarEmbedding.html
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@ -1,18 +1,18 @@
<html><head><!-- Copyright 2007 Aaron Windsor
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<title>Planar Embedding Concept</title>
</head>
<body alink="#ff0000"
bgcolor="#ffffff"
link="#0000ee"
text="#000000"
vlink="#551a8b">
<img src="../../../boost.png" alt="C++ Boost" height="86" width="277">
<body alink="#ff0000"
bgcolor="#ffffff"
link="#0000ee"
text="#000000"
vlink="#551a8b">
<img src="../../../boost.png" alt="C++ Boost" height="86" width="277">
<br clear="">
@ -21,12 +21,12 @@
A planar embedding is an important intermediate representation of a drawing
of a planar graph. Instead of specifying the absolute positions of the vertices
and edges in the plane, a planar embedding specifies their positions relative
to one another. A planar embedding consists of a sequence, for each vertex in
the graph, of all of the edges incident on that vertex in the order in which
and edges in the plane, a planar embedding specifies their positions relative
to one another. A planar embedding consists of a sequence, for each vertex in
the graph, of all of the edges incident on that vertex in the order in which
they are to be drawn around that vertex.
<p>
A planar embedding is a refinement of
A planar embedding is a refinement of
<a href="../../property_map/doc/LvaluePropertyMap.html">LValuePropertyMap</a> that
places additional restrictions the <tt>value_type</tt> used in the property
map.
@ -36,24 +36,24 @@ map.
<table>
<tbody>
<tr>
<td> <tt>Embedding</tt> </td>
<tr>
<td> <tt>Embedding</tt> </td>
<td> is a type that models the Planar Embedding concept.</td>
</tr>
<tr>
<tr>
<td> <tt>embedding</tt> </td>
<td> is an object of type <tt>Embedding</tt>. </td>
</tr>
<tr>
<td> <tt>Graph</tt> </td>
<tr>
<td> <tt>Graph</tt> </td>
<td> is the type of the underlying graph.</td>
</tr>
<tr>
<td> <tt>e</tt> </td>
<td> is an object of type <tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>.
<tr>
<td> <tt>e</tt> </td>
<td> is an object of type <tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>.
</td>
</tr>
@ -63,7 +63,7 @@ map.
</tt>.</td>
</tr><tr>
<td>
<td>
</td></tr></tbody></table>
@ -72,12 +72,12 @@ map.
<table border="1">
<tbody><tr>
<tbody><tr>
<td> Const Iterator </td>
<td> <tt>boost::property_traits&lt;Embedding&gt;::value_type::const_iterator
</tt>
</td>
<td> The iterator type used to iterate over the ordering of the edges in the
<td> The iterator type used to iterate over the ordering of the edges in the
planar embedding of a particular vertex
</td>
</tr>
@ -92,32 +92,32 @@ planar embedding of a particular vertex
<tbody><tr><th>Expression</th><th>Return Type</th><th>Description</th>
</tr><tr>
</tr><tr>
<td> <tt>embedding[v].begin()</tt> </td>
<td> <tt>boost::property_traits&lt;Embedding&gt;::value_type::const_iterator
</tt></td>
<td> Returns an iterator to the beginning of the range of edges in the
<td> Returns an iterator to the beginning of the range of edges in the
embedding around vertex v</td>
</tr>
<tr>
<tr>
<td> <tt>embedding[v].end()</tt> </td>
<td> <tt>boost::property_traits&lt;Embedding&gt;::value_type::const_iterator
</tt></td>
<td> Returns an iterator to the end of the range of edges in the
<td> Returns an iterator to the end of the range of edges in the
embedding around vertex v</td>
</tr>
<tr>
<tr>
<td> <tt>embedding[v].clear()</tt> </td>
<td> <tt>void</tt></td>
<td> Clears all edges in the embedding around a vertex <tt>v</tt></td>
</tr>
<tr>
<tr>
<td> <tt>embedding[v].push_back(e)</tt> </td>
<td> <tt>void</tt></td>
<td> Adds an edge <tt>e</tt> to the end of the sequence of embedded edges
<td> Adds an edge <tt>e</tt> to the end of the sequence of embedded edges
around the vertex <tt>v</tt> </td>
</tr>
@ -126,12 +126,12 @@ planar embedding of a particular vertex
</p><h3>Complexity Guarantees</h3>
Starting with an empty embedding, any mixed sequence of <i>n</i> calls to a
particular vertex's <tt>push_back</tt> and <tt>clear</tt> should take
particular vertex's <tt>push_back</tt> and <tt>clear</tt> should take
<i>O(n)</i> time.
<h3>Models</h3>
Any LValue property map that maps vertices to a <tt>std::vector</tt>,
Any LValue property map that maps vertices to a <tt>std::vector</tt>,
<tt>std::list</tt>, or <tt>std::deque</tt> models this
concept. Below is an example of using this approach to create a model of
PlanarEmbedding:
@ -146,7 +146,7 @@ PlanarEmbedding:
// an instance of Graph in a variable g.
// A typedef for the storage - a vector of vectors of edge descriptors
typedef
typedef
std::vector&lt; std::vector&lt; graph_traits&lt;Graph&gt;::edge_descriptor &gt; &gt;
planar_embedding_storage_t;
@ -173,6 +173,6 @@ planar_embedding_t planar_embedding(planar_embedding_storage.begin(),
<br>
</p><hr>
Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
aaron.windsor@gmail.com</a>)
</body></html>

38
doc/PlanarFaceVisitor.html
View File

@ -1,28 +1,28 @@
<HTML>
<!-- Copyright 2007 Aaron Windsor
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<HEAD>
<TITLE>Planar Face Visitor Concept</TITLE>
</HEAD>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
<H1>Planar Face Visitor Concept</H1>
This concept defines the visitor interface for
<a href="./planar_face_traversal.html"><tt>planar_face_traversal</tt></a>.
Users can define a class with the Planar Face Visitor interface and pass an
object of the class to <tt>planar_face_traversal</tt>, thereby augmenting the
actions taken during the traversal. Note that objects passed to
This concept defines the visitor interface for
<a href="./planar_face_traversal.html"><tt>planar_face_traversal</tt></a>.
Users can define a class with the Planar Face Visitor interface and pass an
object of the class to <tt>planar_face_traversal</tt>, thereby augmenting the
actions taken during the traversal. Note that objects passed to
<tt>planar_face_traversal</tt> are passed by reference.
<h3>Notation</h3>
@ -79,8 +79,8 @@ This is invoked once per traversal, before the traversal begins.
<td><tt>vis.begin_face()</tt></td>
<td><tt>void</tt></td>
<td>
This is invoked once for each face, before any vertices or edges on the face
are visited.
This is invoked once for each face, before any vertices or edges on the face
are visited.
</td>
</tr>
@ -108,7 +108,7 @@ This is invoked when an edge is encountered while traversing a face.
<td><tt>vis.end_face()</tt></td>
<td><tt>void</tt></td>
<td>
This is invoked once for each face, after all vertices and edges on the face
This is invoked once for each face, after all vertices and edges on the face
are visited.
</td>
</tr>
@ -129,13 +129,13 @@ This is invoked once per traversal, after the traversal ends.
<ul>
<li> The file <a href="../../../boost/graph/planar_face_traversal.hpp">
<tt>planar_face_traversal.hpp</tt></a> contains a class
<tt>planar_face_traversal.hpp</tt></a> contains a class
<tt>planar_face_traversal_visitor</tt> that implements empty actions for
all event points of a Planar Face Visitor. In the case where only a few of the
all event points of a Planar Face Visitor. In the case where only a few of the
event points of Planar Face Visitor need to be implemented, one can derive from
<tt>planar_face_traversal_visitor</tt> and only implement the necessary event
<tt>planar_face_traversal_visitor</tt> and only implement the necessary event
points. <li> The implementation of <a href="./make_maximal_planar.html">
<tt>make_maximal_planar</tt></a> uses a <tt>triangulation_visitor</tt> that is
<tt>make_maximal_planar</tt></a> uses a <tt>triangulation_visitor</tt> that is
a model of Planar Face Visitor.
</li>
</ul>
@ -145,4 +145,4 @@ a model of Planar Face Visitor.
Copyright &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
</BODY>
</HTML>
</HTML>

14
doc/PropertyGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>PropertyGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -90,7 +90,7 @@ function which returns a property map object.
<td><pre>boost::property_map&lt;G, PropertyTag&gt;::type</pre>
The type of the property map for the property specified by
<TT>PropertyTag</TT>. This type must be a model of <a
href="../../property_map/doc/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
href="../../property_map/doc/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
with a key type the same as the graph's vertex or edge descriptor type.
</td>
</tr>
@ -207,4 +207,4 @@ The <tt>get()</tt> property map function must be constant time.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/PropertyTag.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Property</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -67,7 +67,7 @@ href="../../../boost/pending/property.hpp"><tt>boost/pending/property.hpp</tt></
<h3>Refinement of</h3>
<a
href="http://www.boost.org/sgi/stl/DefaultConstructible.html">Default Constructible</a>
href="http://www.boost.org/sgi/stl/DefaultConstructible.html">Default Constructible</a>
<h3>Models</h3>
@ -114,4 +114,4 @@ type is also required to specialize
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

10
doc/UpdatableQueue.html
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@ -9,7 +9,7 @@
<head>
<title>UpdatableQueue</title>
</head>
<body>
<body>
<img src="../../../boost.png" alt="C++ Boost">
<h2><a name="concept:UpdatableQueue">UpdatableQueue</a></h2>
@ -30,7 +30,7 @@
<h3>Members</h3>
For a type to model the UpdatableQueue concept it must have the following members
For a type to model the UpdatableQueue concept it must have the following members
in addition to the members that are required of types that model <a href="./Buffer.html">Buffer</a>:
<p>
@ -59,14 +59,14 @@ in addition to the members that are required of types that model <a href="./Buff
{
void constraints() {
BOOST_CONCEPT_ASSERT(( Buffer&lt;Q&gt; ));
q.update(g_ct);
}
void const_constraints(const Q&amp; cq) {
if (cq.contains(g_ct));
}
static const typename Buffer&lt;Q&gt;::value_type g_ct;
Q q;
};

14
doc/VertexAndEdgeListGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>VertexAndEdgeListGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -27,7 +27,7 @@ requirements are added.
<H3>Refinement of</H3>
<a href="./VertexListGraph.html">VertexListGraph</a>,
<a href="./VertexListGraph.html">VertexListGraph</a>,
<a href="./EdgeListGraph.html">EdgeListGraph</a>
@ -67,4 +67,4 @@ requirements are added.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/VertexListGraph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>VertexListGraph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -118,7 +118,7 @@ groups these requirements together, hence the VertexListGraph concept.
template &lt;class G&gt;
struct VertexListGraphConcept
{
typedef typename boost::graph_traits&lt;G&gt;::vertex_iterator
typedef typename boost::graph_traits&lt;G&gt;::vertex_iterator
vertex_iterator;
void constraints() {
BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept&lt;G&gt; ));
@ -151,4 +151,4 @@ groups these requirements together, hence the VertexListGraph concept.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

18
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Vertex Mutable Graph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -37,7 +37,7 @@ No additional associated types.
<h3>Valid Expressions</h3>
<ul>
<li><a name="sec:add_vertex"><TT>add_vertex(g)</TT></a>
<li><a name="sec:add_vertex"><TT>add_vertex(g)</TT></a>
<b>returns</b> <TT>vertex_descriptor</TT>
<br><br>
@ -56,7 +56,7 @@ No additional associated types.
<br>
<b> Postconditions: </b> <TT>num_vertices(g)</TT> is one less; <i>u</i>
no longer appears in the vertex set of the graph and it
is no longer a valid vertex descriptor.
is no longer a valid vertex descriptor.
</li>
</ul>
@ -64,7 +64,7 @@ No additional associated types.
<H3>Complexity guarantees</H3>
<ul>
<li> Vertex insertion is guaranteed to be amortized constant time.
<li> Vertex removal is at most <TT>O(|E| + |V|)</TT>.
</ul>
@ -79,5 +79,5 @@ No additional associated types.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Acknowledgements</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -73,4 +73,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

2
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@ -1,7 +1,7 @@
<html>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Graph Traits</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -155,4 +155,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

62
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@ -1,23 +1,23 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Adjacency Matrix</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
<H1><A NAME="sec:adjacency-matrix-class"></A>
<pre>
adjacency_matrix&lt;Directed, VertexProperty,
adjacency_matrix&lt;Directed, VertexProperty,
EdgeProperty, GraphProperty,
Allocator&gt;
</pre>
@ -61,7 +61,7 @@ href="adjacency_list.html"><tt>adjacency_list</tt></a>. These may be
<a
href="using_adjacency_list.html#sec:adjacency-list-properties">interior
properties</a>. The types of all property values must be
Copy Constructible, Assignable and Default Constructible.
Copy Constructible, Assignable and Default Constructible.
In the case of an undirected graph, the
<tt>adjacency_matrix</tt>. class does not use a full <i>V x V</i>
@ -83,11 +83,11 @@ matrix representation of an undirected graph.
<h3>Example</h3>
Creating the graph of <a href="#fig:adj-matrix-graph">Figure 1</a>.
Creating the graph of <a href="#fig:adj-matrix-graph">Figure 1</a>.
<pre>
enum { A, B, C, D, E, F, N };
const char* name = "ABCDEF";
typedef boost::adjacency_matrix&lt;boost::directedS> Graph;
Graph g(N);
add_edge(B, C, g);
@ -112,17 +112,17 @@ Creating the graph of <a href="#fig:adj-matrix-graph">Figure 1</a>.
</pre>
The output is:
<pre>
vertex set: A B C D E F
vertex set: A B C D E F
edge set: (B,C) (B,F) (C,A) (C,C) (D,E) (E,D) (F,A)
edge set: (B,C) (B,F) (C,A) (C,C) (D,E) (E,D) (F,A)
out-edges:
A -->
B --> C F
C --> A C
D --> E
E --> D
F --> A
out-edges:
A -->
B --> C F
C --> A C
D --> E
E --> D
F --> A
</pre>
Creating the graph of <a href="#fig:undir-adj-matrix-graph">Figure 2</a>.
@ -152,17 +152,17 @@ Creating the graph of <a href="#fig:undir-adj-matrix-graph">Figure 2</a>.
</pre>
The output is:
<pre>
vertex set: A B C D E F
vertex set: A B C D E F
edge set: (C,A) (C,B) (E,D) (F,A) (F,B)
edge set: (C,A) (C,B) (E,D) (F,A) (F,B)
incident edges:
A &lt;--> C F
B &lt;--> C F
C &lt;--> A B
D &lt;--> E
E &lt;--> D
F &lt;--> A B
incident edges:
A &lt;--> C F
B &lt;--> C F
C &lt;--> A B
D &lt;--> E
E &lt;--> D
F &lt;--> A B
</pre>
@ -205,7 +205,7 @@ The output is:
<h3>Model Of</h3>
<a href="./VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>,
<a href="./VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>,
<a href="./IncidenceGraph.html">Incidence Graph</a>,
<a href="./BidirectionalGraph.html">Bidirectional Graph</a>,
<a
@ -236,7 +236,7 @@ The type for the edge descriptors associated with the
<hr>
<tt>graph_traits&lt;adjacency_matrix&gt;::vertex_iterator</tt>
<br><br>
The type for the iterators returned by <tt>vertices()</tt>.
The type for the iterators returned by <tt>vertices()</tt>.
The vertex iterator models <a href="http://www.boost.org/sgi/stl/RandomAccessIterator.html">RandomAccessIterator</a>. <br>
(Required by <a href="VertexListGraph.html">VertexListGraph</a>.)
@ -420,7 +420,7 @@ degree_size_type
out_degree(vertex_descriptor u, const adjacency_matrix&amp; g)
</pre>
Returns the number of edges leaving vertex <tt>u</tt>.<br>
(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
(Required by <a href="IncidenceGraph.html">IncidenceGraph</a>.)
<hr>
<hr>
@ -440,7 +440,7 @@ degree_size_type
in_degree(vertex_descriptor u, const adjacency_matrix&amp; g)
</pre>
Returns the number of edges entering vertex <tt>u</tt>.<br>
(Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)
(Required by <a href="BidirectionalGraph.html">BidirectionalGraph</a>.)
<hr>
<hr>

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) 2004 Kris Beevers
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: astar_heuristic</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -93,4 +93,4 @@ HREF="mailto:beevek@cs.rpi.edu">beevek@cs.rpi.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) 2004 Kris Beevers
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: A* Heuristic Search</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -309,7 +309,7 @@ IN: <tt>const VertexListGraph&amp; g</tt>
IN: <tt>const IncidenceGraph&amp; g</tt>
<blockquote>
The graph object on which the algorithm will be applied for <tt>astar_search_no_init()</tt>. The type
<tt>IncidenceGraph</tt> must be a model of the
<tt>IncidenceGraph</tt> must be a model of the
<a href="IncidenceGraph.html">Incidence Graph</a>
concept.
</blockquote>
@ -586,4 +586,4 @@ HREF="mailto:beevek@cs.rpi.edu">beevek@cs.rpi.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) 2004 Kris Beevers
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: astar_visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -105,4 +105,4 @@ HREF="mailto:beevek@cs.rpi.edu">beevek@cs.rpi.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Bandwidth</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -90,4 +90,4 @@ of the i-th bandwidths <i>B<sub>i</sub>(G)</i>.<br>
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

20
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@ -1,7 +1,7 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<!--
Copyright (c) 2004 Trustees of Indiana University
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
@ -18,7 +18,7 @@
<div class="titlepage"></div>
<div class="refnamediv">
<IMG SRC="../../../boost.png"
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<h1><img src="figs/python.gif" alt="(Python)"/><span class="refentrytitle">Function
@ -36,23 +36,23 @@ clustering based on edge betweenness centrality.</p>
<span class="bold"><b>template</b></span>&lt;<span class=
"bold"><b>typename</b></span> MutableGraph, <span class=
"bold"><b>typename</b></span> Done, <span class=
"bold"><b>typename</b></span> EdgeCentralityMap,
"bold"><b>typename</b></span> EdgeCentralityMap,
<span class=
"bold"><b>typename</b></span> VertexIndexMap&gt;
"bold"><b>typename</b></span> VertexIndexMap&gt;
<span class="type"><span class=
"bold"><b>void</b></span></span> betweenness_centrality_clustering(MutableGraph &amp; g, Done done,
EdgeCentralityMap edge_centrality,
"bold"><b>void</b></span></span> betweenness_centrality_clustering(MutableGraph &amp; g, Done done,
EdgeCentralityMap edge_centrality,
VertexIndexMap vertex_index);
<span class="bold"><b>template</b></span>&lt;<span class=
"bold"><b>typename</b></span> MutableGraph, <span class=
"bold"><b>typename</b></span> Done, <span class=
"bold"><b>typename</b></span> EdgeCentralityMap&gt;
"bold"><b>typename</b></span> EdgeCentralityMap&gt;
<span class="type"><span class=
"bold"><b>void</b></span></span> betweenness_centrality_clustering(MutableGraph &amp; g, Done done,
"bold"><b>void</b></span></span> betweenness_centrality_clustering(MutableGraph &amp; g, Done done,
EdgeCentralityMap edge_centrality);
<span class="bold"><b>template</b></span>&lt;<span class=
"bold"><b>typename</b></span> MutableGraph, <span class=
"bold"><b>typename</b></span> Done&gt;
"bold"><b>typename</b></span> Done&gt;
<span class="type"><span class=
"bold"><b>void</b></span></span> betweenness_centrality_clustering(MutableGraph &amp; g, Done done);
</pre></div>
@ -108,7 +108,7 @@ OUT/UTIL: <tt>EdgeCentralityMap edge_centrality_map</tt>
<b>Python default</b>: <tt>graph.get_edge_double_map("centrality")</tt>
</blockquote>
IN: <tt>VertexIndexMap vertex_index</tt>
IN: <tt>VertexIndexMap vertex_index</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(g))</tt>. This is necessary for efficient updates of the

54
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Bellman Ford Shortest Paths</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -24,7 +24,7 @@
<PRE>
<i>// named paramter version</i>
template &lt;class <a href="./EdgeListGraph.html">EdgeListGraph</a>, class Size, class P, class T, class R&gt;
bool bellman_ford_shortest_paths(const EdgeListGraph&amp; g, Size N,
bool bellman_ford_shortest_paths(const EdgeListGraph&amp; g, Size N,
const bgl_named_params&lt;P, T, R&gt;&amp; params = <i>all defaults</i>);
template &lt;class <a href="./VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>, class P, class T, class R&gt;
@ -36,8 +36,8 @@ template &lt;class <a href="./EdgeListGraph.html">EdgeListGraph</a>, class Size,
class PredecessorMap, class DistanceMap,
class <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">BinaryFunction</a>, class <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">BinaryPredicate</a>,
class <a href="./BellmanFordVisitor.html">BellmanFordVisitor</a>&gt;
bool bellman_ford_shortest_paths(EdgeListGraph&amp; g, Size N,
WeightMap weight, PredecessorMap pred, DistanceMap distance,
bool bellman_ford_shortest_paths(EdgeListGraph&amp; g, Size N,
WeightMap weight, PredecessorMap pred, DistanceMap distance,
BinaryFunction combine, BinaryPredicate compare, BellmanFordVisitor v)
</PRE>
@ -51,7 +51,7 @@ shortest paths problem for a graph with both positive and negative
edge weights. For the definition of the shortest paths problem see
Section <A
HREF="./graph_theory_review.html#sec:shortest-paths-algorithms">Shortest-Paths
Algorithms</A>.
Algorithms</A>.
If you only need to solve the shortest paths problem for positive edge
weights, Dijkstra's algorithm provides a more efficient
alternative. If all the edge weights are all equal to one then breadth-first
@ -77,7 +77,7 @@ ultimately be the parent in the shortest paths tree
<td valign="top">
<pre>
RELAX(<i>u</i>, <i>v</i>, <i>w</i>, <i>d</i>, <i>p</i>)
<b>if</b> (<i>w(u,v) + d[u] < d[v]</i>)
<b>if</b> (<i>w(u,v) + d[u] < d[v]</i>)
<i>d[v] := w(u,v) + d[u]</i>
<i>p[v] := u</i>
<b>else</b>
@ -91,7 +91,7 @@ RELAX(<i>u</i>, <i>v</i>, <i>w</i>, <i>d</i>, <i>p</i>)
relax edge <i>(u,v)</i>
edge <i>(u,v)</i> is not relaxed
edge <i>(u,v)</i> is not relaxed
</pre>
</td>
</tr>
@ -115,19 +115,19 @@ otherwise.
<pre>
BELLMAN-FORD(<i>G</i>)
<i>// Optional initialization</i>
<b>for</b> each vertex <i>u in V</i>
<b>for</b> each vertex <i>u in V</i>
<i>d[u] := infinity</i>
<i>p[u] := u</i>
<i>p[u] := u</i>
<b>end for</b>
<b>for</b> <i>i := 1</i> <b>to</b> <i>|V|-1</i>
<b>for</b> each edge <i>(u,v) in E</i>
<b>for</b> <i>i := 1</i> <b>to</b> <i>|V|-1</i>
<b>for</b> each edge <i>(u,v) in E</i>
RELAX(<i>u</i>, <i>v</i>, <i>w</i>, <i>d</i>, <i>p</i>)
<b>end for</b>
<b>end for</b>
<b>for</b> each edge <i>(u,v) in E</i>
<b>for</b> each edge <i>(u,v) in E</i>
<b>if</b> (<i>w(u,v) + d[u] < d[v]</i>)
<b>return</b> (false, , )
<b>else</b>
<b>else</b>
...
<b>end for</b>
<b>return</b> (true, <i>p</i>, <i>d</i>)
@ -148,9 +148,9 @@ examine edge <i>(u,v)</i>
edge <i>(u,v)</i> was not minimized
edge <i>(u,v)</i> was not minimized
edge <i>(u,v)</i> was minimized
edge <i>(u,v)</i> was minimized
</pre>
</td>
</tr>
@ -175,7 +175,7 @@ algorithm's event points.
<h3>Parameters</h3>
IN: <tt>EdgeListGraph&amp; g</tt>
IN: <tt>EdgeListGraph&amp; g</tt>
<blockquote>
A directed or undirected graph whose type must be a model of
<a href="./EdgeListGraph.html">Edge List Graph</a>. If a root vertex is
@ -211,7 +211,7 @@ IN: <tt>weight_map(WeightMap w)</tt>
<b>Python default</b>: <tt>graph.get_edge_double_map("weight")</tt>
</blockquote>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<blockquote>
The predecessor map records the edges in the minimum spanning
tree. Upon completion of the algorithm, the edges <i>(p[u],u)</i>
@ -227,7 +227,7 @@ OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<b>Python</b>: Must be a <tt>vertex_vertex_map</tt> for the graph.<br>
</blockquote>
IN/OUT: <tt>distance_map(DistanceMap d)</tt>
IN/OUT: <tt>distance_map(DistanceMap d)</tt>
<blockquote>
The shortest path weight from the source vertex to each vertex in
the graph <tt>g</tt> is recorded in this property map. The type
@ -307,11 +307,11 @@ The time complexity is <i>O(V E)</i>.
<li><b><tt>vis.examine_edge(e, g)</tt></b> is invoked on every edge in
the graph <i>|V|</i> times.
<li><b><tt>vis.edge_relaxed(e, g)</tt></b> is invoked when the distance
label for the target vertex is decreased. The edge <i>(u,v)</i> that
label for the target vertex is decreased. The edge <i>(u,v)</i> that
participated in the last relaxation for vertex <i>v</i> is an edge in the
shortest paths tree.
shortest paths tree.
<li><b><tt>vis.edge_not_relaxed(e, g)</tt></b> is invoked if the distance label
for the target vertex is not decreased.
for the target vertex is not decreased.
<li><b><tt>vis.edge_minimized(e, g)</tt></b> is invoked during the
second stage of the algorithm, during the test of whether each edge
was minimized. If the edge is minimized then this function
@ -330,7 +330,7 @@ href="../example/bellman-example.cpp"><TT>examples/bellman-example.cpp</TT></a>.
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -346,4 +346,4 @@ href="../example/bellman-example.cpp"><TT>examples/bellman-example.cpp</TT></a>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: bellman_visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -108,4 +108,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -2,7 +2,7 @@
<html>
<!--
Copyright (c) 2004 Trustees of Indiana University
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
@ -12,54 +12,54 @@
</head>
<body>
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<h1><img src="figs/python.gif" alt="(Python)"/><tt>brandes_betweenness_centrality</tt></h1>
<p>
<pre>
<em>// named parameter versions</em>
template&lt;typename Graph, typename Param, typename Tag, typename Rest&gt;
void
void
brandes_betweenness_centrality(const Graph&amp; g,
const bgl_named_params&lt;Param,Tag,Rest&gt;&amp; params);
template&lt;typename Graph, typename CentralityMap&gt;
void
void
brandes_betweenness_centrality(const Graph&amp; g, CentralityMap centrality_map);
template&lt;typename Graph, typename CentralityMap, typename EdgeCentralityMap&gt;
void
void
brandes_betweenness_centrality(const Graph&amp; g, CentralityMap centrality_map,
EdgeCentralityMap edge_centrality);
<em>// non-named parameter versions</em>
template&lt;typename Graph, typename CentralityMap, typename EdgeCentralityMap,
typename IncomingMap, typename DistanceMap, typename DependencyMap,
typename IncomingMap, typename DistanceMap, typename DependencyMap,
typename PathCountMap, typename VertexIndexMap&gt;
void
void
brandes_betweenness_centrality(const Graph&amp; g, CentralityMap centrality_map,
EdgeCentralityMap edge_centrality,
IncomingMap incoming,
DistanceMap distance, DependencyMap dependency,
PathCountMap path_count,
PathCountMap path_count,
VertexIndexMap vertex_index);
template&lt;typename Graph, typename CentralityMap, typename EdgeCentralityMap,
typename IncomingMap, typename DistanceMap, typename DependencyMap,
typename PathCountMap, typename VertexIndexMap, typename WeightMap&gt;
void
typename IncomingMap, typename DistanceMap, typename DependencyMap,
typename PathCountMap, typename VertexIndexMap, typename WeightMap&gt;
void
brandes_betweenness_centrality(const Graph&amp; g, CentralityMap centrality_map,
EdgeCentralityMap edge_centrality,
IncomingMap incoming,
IncomingMap incoming,
DistanceMap distance, DependencyMap dependency,
PathCountMap path_count,
PathCountMap path_count,
VertexIndexMap vertex_index,
WeightMap weight_map);
<em>// helper functions</em>
template&lt;typename Graph, typename CentralityMap&gt;
void
void
relative_betweenness_centrality(const Graph&amp; g, CentralityMap centrality_map);
template&lt;typename Graph, typename CentralityMap&gt;
@ -137,8 +137,8 @@ IN: <tt>const Graph&amp; g</tt>
<b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>
UTIL: <tt>IncomingMap incoming</tt>
UTIL: <tt>IncomingMap incoming</tt>
<blockquote>
This property map records the set of edges incoming to each vertex that comprise a shortest path from a particular source vertex through this vertex, and is used internally by the algorithm.The <tt>IncomingMap</tt> type must be a <a
href="../../property_map/doc/LvaluePropertyMap.html">Lvalue Property
@ -155,7 +155,7 @@ UTIL: <tt>IncomingMap incoming</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL: <tt>DistanceMap distance_map</tt>
UTIL: <tt>DistanceMap distance_map</tt>
<blockquote>
The shortest path weight from each source vertex <tt>s</tt> to each
vertex in the graph <tt>g</tt> is recorded in this property map, but
@ -178,7 +178,7 @@ UTIL: <tt>DistanceMap distance_map</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL: <tt>DependencyMap dependency</tt>
UTIL: <tt>DependencyMap dependency</tt>
<blockquote>
Property map used internally to accumulate partial betweenness
centrality results. The type <tt>DependencyMap</tt> must be a model
@ -198,7 +198,7 @@ UTIL: <tt>DependencyMap dependency</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL: <tt>PathCountMap path_count</tt>
UTIL: <tt>PathCountMap path_count</tt>
<blockquote>
Property map used internally to accumulate the number of paths that
pass through each particular vertex. The type <tt>PathCountMap</tt>
@ -254,7 +254,7 @@ OUT/UTIL: <tt>EdgeCentralityMap edge_centrality_map</tt>
<b>Python default</b>: <tt>graph.get_edge_double_map("centrality")</tt>
</blockquote>
IN: <tt>vertex_index_map(VertexIndexMap vertex_index)</tt>
IN: <tt>vertex_index_map(VertexIndexMap vertex_index)</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(g))</tt>. This is necessary for efficient updates of the
@ -271,11 +271,11 @@ IN: <tt>vertex_index_map(VertexIndexMap vertex_index)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>weight_map(WeightMap w_map)</tt>
IN: <tt>weight_map(WeightMap w_map)</tt>
<blockquote>
The weight or ``length'' of each edge in the graph. The weights
must all be non-negative, and the algorithm will throw a
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
exception is one of the edges is negative.
The type <tt>WeightMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of
@ -286,7 +286,7 @@ IN: <tt>weight_map(WeightMap w_map)</tt>
<b>Python</b>: If supplied, must be an <tt>edge_double_map</tt> for the graph.
</blockquote>
<h3>Complexity</h3>
<h3>Complexity</h3>
The time complexity is <em>O(VE)</em> for unweighted graphs and
<em>O(VE + V(V+E) log V)</em> for weighted graphs. The space complexity
is <em>O(VE)</em>.

16
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: bfs_visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -38,10 +38,10 @@ visitor.
<pre>
// Construct graph G and obtain the source vertex s ...
boost::breadth_first_search(G, s,
boost::breadth_first_search(G, s,
boost::make_bfs_visitor(
std::make_pair(boost::record_distances(d, boost::on_tree_edge()),
std::make_pair(boost::record_predecessors(p.begin(),
std::make_pair(boost::record_predecessors(p.begin(),
boost::on_tree_edge()),
copy_graph(G_copy, boost::on_examine_edge())))) );
</pre>
@ -125,4 +125,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Named Parameters</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -38,7 +38,7 @@ reasons:
he or she has to resort to providing all the parameters.
<li>Since the list of parameters is long, it is easy to forget
the ordering.
the ordering.
</ul>
<p>
@ -54,7 +54,7 @@ indicates which parameter the argument is for. Each of the named
parameters is separated by a <b>period</b>, not a comma.
<pre>
bool r = boost::bellman_ford_shortest_paths(g, int(N),
bool r = boost::bellman_ford_shortest_paths(g, int(N),
boost::weight_map(weight).
distance_map(&amp;distance[0]).
predecessor_map(&amp;parent[0]));
@ -66,7 +66,7 @@ an call to <tt>bellman_ford_shortest_paths</tt> that is equivalent to
the one above.
<pre>
bool r = boost::bellman_ford_shortest_paths(g, int(N),
bool r = boost::bellman_ford_shortest_paths(g, int(N),
boost::predecessor_map(&amp;parent[0]).
distance_map(&amp;distance[0]).
weight_map(weight));

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Bibliography</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -264,7 +264,7 @@ SIAM Journal on Computing, 1(2):146-160, 1972
<P></P><DT><A NAME="eppstein97:dynamic_graph">42</a>
<DD>David Eppstein, Zvi Galil, and Giuseppe F. Italiano<BR>
<EM>Dynamic Graph Algorithms.</EM><br>
Chapter 22, CRC Handbook of Algorithms and Theory of Computation, 1997.
Chapter 22, CRC Handbook of Algorithms and Theory of Computation, 1997.
<P></P><DT><A NAME="cuthill69:reducing_bandwith">43</a>
<DD>E. Cuthill and J. McKee<BR>
@ -330,7 +330,7 @@ BIT, 10, 1970, pp. 76-94.
<p></p><dt><a name="brandes01">54</a>
<dd>Ulrik Brandes<br>
<em><a href="http://ella.slis.indiana.edu/~katy/L579/brandes.pdf">A
<em><a href="http://ella.slis.indiana.edu/~katy/L579/brandes.pdf">A
Faster Algorithm for Betweenness Centrality</a></em><br>
Journal of Mathematical Sociology 25 (2):163-177, 2001.
@ -347,7 +347,7 @@ Technical Report BN9/71, Stichting Mahtematisch Centrum, Amsterdam, 1971.
<p></p><dt><a name="kamada89">57</a>
<dd>T. Kamada and S. Kawai<br>
<em>An algorithm for drawing general undirected graphs.</em><br>
Information Processing Letters, 31, pp. 7-15, 1989.
Information Processing Letters, 31, pp. 7-15, 1989.
<p></p><dt><a name="fruchterman91">58</a>
<dd>T. Fruchterman and E. Reingold<br>
@ -454,7 +454,7 @@ Journal of the ACM (JACM), 23(2): 221-234, 1976.
Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 434-443, 1990.
</dl>
<br>
<HR>
<TABLE>
@ -464,4 +464,4 @@ Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 4
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,21 +1,21 @@
<HTML>
<!--
Copyright 2001-2004 The Trustees of Indiana University.
Use, modification and distribution is subject to the Boost Software
License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
Authors: Douglas Gregor
Jeremy Siek
Andrew Lumsdaine
-->
<Head>
<Title>Boost Graph Library: Biconnected Components and Articulation Points</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -25,7 +25,7 @@
<A NAME="sec:biconnected-components">biconnected_components
</A>
</TT>
and
and
<tt>articulation_points</tt>
</h1>
@ -34,25 +34,25 @@ and
template &lt;typename Graph, typename ComponentMap, typename OutputIterator,
typename P, typename T, typename R&gt;
std::pair&lt;std::size_t, OutputIterator&gt;
biconnected_components(const Graph& g, ComponentMap comp, OutputIterator out,
biconnected_components(const Graph& g, ComponentMap comp, OutputIterator out,
const bgl_named_params&lt;P, T, R&gt;&amp; params)
template &lt;typename Graph, typename ComponentMap,
typename P, typename T, typename R&gt;
std::size_t
biconnected_components(const Graph& g, ComponentMap comp,
biconnected_components(const Graph& g, ComponentMap comp,
const bgl_named_params&lt;P, T, R&gt;&amp; params)
template &lt;typename Graph, typename OutputIterator,
template &lt;typename Graph, typename OutputIterator,
typename P, typename T, typename R&gt;
OutputIterator articulation_points(const Graph& g, OutputIterator out,
OutputIterator articulation_points(const Graph& g, OutputIterator out,
const bgl_named_params&lt;P, T, R&gt;&amp; params)
<i>// non-named parameter version</i>
template &lt;typename Graph, typename ComponentMap, typename OutputIterator,
typename DiscoverTimeMap, typename LowPointMap&gt;
std::pair&lt;std::size_t, OutputIterator&gt;
biconnected_components(const Graph& g, ComponentMap comp, OutputIterator out,
biconnected_components(const Graph& g, ComponentMap comp, OutputIterator out,
DiscoverTimeMap discover_time, LowPointMap lowpt);
template &lt;typename Graph, typename ComponentMap, typename OutputIterator&gt;
@ -142,10 +142,10 @@ points.
<h3>Named Parameters</h3>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(g))</tt>. The type
num_vertices(g))</tt>. The type
<tt>VertexIndexMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The value type of the map must be an
integer type. The vertex descriptor type of the graph needs to be
@ -192,9 +192,9 @@ UTIL/OUT: <tt>lowpoint_map(LowPointMap lowpt)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL/OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
UTIL/OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<blockquote>
The predecessor map records the depth first search tree.
The predecessor map records the depth first search tree.
The <tt>PredecessorMap</tt> type
must be a <a
href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
@ -241,7 +241,7 @@ articulation points of an undirected graph.
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -260,4 +260,4 @@ HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)<br>
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -5,7 +5,7 @@
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{latexsym}
\usepackage{jweb}
\usepackage{times}
\usepackage{graphicx}
@ -358,7 +358,7 @@ int main()
% \paragraph{Definition.} A \emph{palm tree} $P$ is a directed graph that
% \paragraph{Definition.} A \emph{palm tree} $P$ is a directed graph that
% consists of two disjoint sets of edges, denoted by $v \rightarrow w$
% and $v \backedge w$ respectively, with the following properties:

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@ -1,39 +1,39 @@
<HTML>
<!-- Copyright 2007 Aaron Windsor
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Boyer-Myrvold Planarity Testing/Embedding</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
<H1>Boyer-Myrvold Planarity Testing/Embedding</H1>
<p>
A graph is <a href="./planar_graphs.html#planar"><i>planar</i></a> if it can
be drawn in two-dimensional space without any of its edges crossing. Such a
drawing of a planar graph is called a
<a href="./planar_graphs.html#plane_drawing"><i>plane drawing</i></a>. Each
A graph is <a href="./planar_graphs.html#planar"><i>planar</i></a> if it can
be drawn in two-dimensional space without any of its edges crossing. Such a
drawing of a planar graph is called a
<a href="./planar_graphs.html#plane_drawing"><i>plane drawing</i></a>. Each
plane drawing belongs to an equivalence class called a <i>planar embedding</i>
<a href="#1">[1]</a> that is defined by the clockwise ordering of adjacent
edges around each vertex in the graph. A planar embedding is a convenient
intermediate representation of an actual drawing of a planar graph, and many
planar graph drawing algorithms are formulated as functions mapping a planar
<a href="#1">[1]</a> that is defined by the clockwise ordering of adjacent
edges around each vertex in the graph. A planar embedding is a convenient
intermediate representation of an actual drawing of a planar graph, and many
planar graph drawing algorithms are formulated as functions mapping a planar
embedding to a plane drawing.
<br>
<br>
<table align="center" class="image">
<caption align="bottom"><h5>A planar graph (top left), along with a planar
embedding of that graph (bottom left) can be used to create a plane drawing
(right) by embedding edges around each vertex in the order in which they
<caption align="bottom"><h5>A planar graph (top left), along with a planar
embedding of that graph (bottom left) can be used to create a plane drawing
(right) by embedding edges around each vertex in the order in which they
appear in the planar embedding.
</h5></caption>
<tr><td>
@ -44,16 +44,16 @@ appear in the planar embedding.
</table>
<br>
<p>
The function <tt>boyer_myrvold_planarity_test</tt> implements the planarity
testing/embedding algorithm of Boyer and Myrvold
The function <tt>boyer_myrvold_planarity_test</tt> implements the planarity
testing/embedding algorithm of Boyer and Myrvold
[<a href="./bibliography.html#boyermyrvold04">70</a>].
<tt>boyer_myrvold_planarity_test</tt> returns <tt>true</tt> if the input graph
<tt>boyer_myrvold_planarity_test</tt> returns <tt>true</tt> if the input graph
is planar and <tt>false</tt> otherwise. As a side-effect of this test, a planar
embedding can be constructed if the graph is planar or a minimal set of edges
that form a <a href = "./planar_graphs.html#kuratowskisubgraphs">Kuratowski
embedding can be constructed if the graph is planar or a minimal set of edges
that form a <a href = "./planar_graphs.html#kuratowskisubgraphs">Kuratowski
subgraph</a> can be found if the graph is not planar.
<tt>boyer_myrvold_planarity_test</tt> uses named parameter arguments (courtesy
of the <a href="../../parameter/doc/html/index.html">Boost.Parameter</a>
<tt>boyer_myrvold_planarity_test</tt> uses named parameter arguments (courtesy
of the <a href="../../parameter/doc/html/index.html">Boost.Parameter</a>
library) to specify what the function actually does. Some examples are:
<ul>
@ -65,8 +65,8 @@ bool is_planar = boyer_myrvold_planarity_test(g);
<li>Computing a planar embedding for a graph if it is planar, otherwise finding
a set of edges that forms an obstructing Kuratowski subgraph:
<pre>
if (boyer_myrvold_planarity_test(boyer_myrvold_params::graph = g,
boyer_myrvold_params::embedding = embedding_pmap,
if (boyer_myrvold_planarity_test(boyer_myrvold_params::graph = g,
boyer_myrvold_params::embedding = embedding_pmap,
boyer_myrvold_params::kuratowski_subgraph = out_itr
)
)
@ -81,81 +81,81 @@ else
</ul>
<p>
The parameters passed to <tt>boyer_myrvold_planarity_test</tt> in the examples
above do more than just carry the data structures used for input and output -
the algorithm is optimized at compile time based on which parameters are
present. A complete list of parameters accepted and their interactions are
described below.
The parameters passed to <tt>boyer_myrvold_planarity_test</tt> in the examples
above do more than just carry the data structures used for input and output -
the algorithm is optimized at compile time based on which parameters are
present. A complete list of parameters accepted and their interactions are
described below.
<p>
<tt>boyer_myrvold_planarity_test</tt> accepts as input any undirected graph,
even those with self-loops and multiple edges.
However, many planar graph drawing algorithms make additional restrictions
on the structure of the input graph - for example, requiring that the input
However, many planar graph drawing algorithms make additional restrictions
on the structure of the input graph - for example, requiring that the input
graph is connected, biconnected, or even maximal planar (triangulated.)
Fortunately, any planar graph on <i>n</i> vertices that lacks one of these
properties can be augmented with additional edges so that it satisfies that
property in <i>O(n)</i> time - the functions
Fortunately, any planar graph on <i>n</i> vertices that lacks one of these
properties can be augmented with additional edges so that it satisfies that
property in <i>O(n)</i> time - the functions
<tt><a href="./make_connected.html">make_connected</a></tt>,
<tt><a href="./make_biconnected_planar.html">make_biconnected_planar</a></tt>,
and <tt><a href="./make_maximal_planar.html">make_maximal_planar</a></tt>
exist for this purpose. If the graph drawing algorithm you're using requires,
say, a biconnected graph, then you must make your input graph biconnected
<tt><a href="./make_biconnected_planar.html">make_biconnected_planar</a></tt>,
and <tt><a href="./make_maximal_planar.html">make_maximal_planar</a></tt>
exist for this purpose. If the graph drawing algorithm you're using requires,
say, a biconnected graph, then you must make your input graph biconnected
<i>before</i> passing it into <tt>boyer_myrvold_planarity_test</tt> so that the
computed planar embedding includes these additional edges. This may require
more than one call to <tt>boyer_myrvold_planarity_test</tt> depending on the
structure of the graph you begin with, since both
<tt>make_biconnected_planar</tt> and <tt>make_maximal_planar</tt> require a
computed planar embedding includes these additional edges. This may require
more than one call to <tt>boyer_myrvold_planarity_test</tt> depending on the
structure of the graph you begin with, since both
<tt>make_biconnected_planar</tt> and <tt>make_maximal_planar</tt> require a
planar embedding of the existing graph as an input parameter.
<p><p>
The named parameters accepted by <tt>boyer_myrvold_planarity_test</tt> are:
<ul>
<li><b><tt>graph</tt></b> : The input graph - this is the only required
<li><b><tt>graph</tt></b> : The input graph - this is the only required
parameter.
<li><b><tt>vertex_index_map</tt></b> : A mapping from vertices of the input
graph to indexes in the range <tt>[0..num_vertices(g))</tt>. If this parameter
<li><b><tt>vertex_index_map</tt></b> : A mapping from vertices of the input
graph to indexes in the range <tt>[0..num_vertices(g))</tt>. If this parameter
is not provided, the vertex index map is assumed to be available as an interior
property of the graph, accessible by calling <tt>get(vertex_index, g)</tt>.
<li><b><tt>edge_index_map</tt></b>: A mapping from the edges of the input graph
to indexes in the range <tt>[0..num_edges(g))</tt>. This parameter is only
needed if the <tt>kuratowski_subgraph</tt> argument is provided. If the
to indexes in the range <tt>[0..num_edges(g))</tt>. This parameter is only
needed if the <tt>kuratowski_subgraph</tt> argument is provided. If the
<tt>kuratowski_subgraph</tt> argument is provided and this parameter is not
provided, the EdgeIndexMap is assumed to be available as an interior property
provided, the EdgeIndexMap is assumed to be available as an interior property
accessible by calling <tt>get(edge_index, g)</tt>.
<li><b><tt>embedding</tt></b> : If the graph is planar, this will be populated
with a mapping from vertices to the clockwise order of neighbors in the planar
<li><b><tt>embedding</tt></b> : If the graph is planar, this will be populated
with a mapping from vertices to the clockwise order of neighbors in the planar
embedding.
<li><b><tt>kuratowski_subgraph</tt></b> : If the graph is not planar, a minimal
set of edges that form the obstructing Kuratowski subgraph will be written to
set of edges that form the obstructing Kuratowski subgraph will be written to
this iterator.
</ul>
These named parameters all belong to the namespace
<tt>boyer_myrvold_params</tt>. See below for more information on the concepts
required for these arguments.
These named parameters all belong to the namespace
<tt>boyer_myrvold_params</tt>. See below for more information on the concepts
required for these arguments.
<H3>Verifying the output</H3>
Whether or not the input graph is planar, <tt>boyer_myrvold_planarity_test</tt>
can produce a certificate that can be automatically checked to verify that the
function is working properly.
can produce a certificate that can be automatically checked to verify that the
function is working properly.
<p>
If the graph is planar, a planar embedding can be produced. The
planar embedding can be verified by passing it to a plane drawing routine
planar embedding can be verified by passing it to a plane drawing routine
(such as <tt><a href="straight_line_drawing.html">
chrobak_payne_straight_line_drawing</a></tt>) and using the function
<tt><a href="is_straight_line_drawing.html">is_straight_line_drawing</a></tt>
chrobak_payne_straight_line_drawing</a></tt>) and using the function
<tt><a href="is_straight_line_drawing.html">is_straight_line_drawing</a></tt>
to verify that the resulting graph is planar.
<p>
If the graph is not planar, a set of edges that forms a Kuratowski subgraph in
the original graph can be produced. This set of edges can be passed to the
If the graph is not planar, a set of edges that forms a Kuratowski subgraph in
the original graph can be produced. This set of edges can be passed to the
function <tt><a href="is_kuratowski_subgraph.html">is_kuratowski_subgraph</a>
</tt> to verify that they can be contracted into a <i>K<sub>5</sub></i> or
<i>K<sub>3,3</sub></i>. <tt>boyer_myrvold_planarity_test</tt> chooses the set
of edges forming the Kuratowski subgraph in such a way that the contraction to
a <i>K<sub>5</sub></i> or <i>K<sub>3,3</sub></i> can be done by a simple
deterministic process which is described in the documentation to
</tt> to verify that they can be contracted into a <i>K<sub>5</sub></i> or
<i>K<sub>3,3</sub></i>. <tt>boyer_myrvold_planarity_test</tt> chooses the set
of edges forming the Kuratowski subgraph in such a way that the contraction to
a <i>K<sub>5</sub></i> or <i>K<sub>3,3</sub></i> can be done by a simple
deterministic process which is described in the documentation to
<tt>is_kuratowski_subgraph</tt>.
<H3>Where Defined</H3>
@ -170,8 +170,8 @@ deterministic process which is described in the documentation to
IN: <tt>Graph&amp; g</tt>
<blockquote>
Any undirected graph. The graph type must be a model of
<a href="VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a> and
Any undirected graph. The graph type must be a model of
<a href="VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a> and
<a href="IncidenceGraph.html">IncidenceGraph</a>.
</blockquote>
@ -184,7 +184,7 @@ Must model the <a href="PlanarEmbedding.html">PlanarEmbedding</a> concept.
IN <tt>OutputIterator kuratowski_subgraph</tt>
<blockquote>
An OutputIterator which accepts values of the type
An OutputIterator which accepts values of the type
<tt>graph_traits&lt;Graph&gt;::edge_descriptor</tt>
</blockquote>
@ -192,7 +192,7 @@ IN <tt>VertexIndexMap vm</tt>
<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps vertices from <tt>g</tt> to distinct integers in the range
</a> that maps vertices from <tt>g</tt> to distinct integers in the range
<tt>[0, num_vertices(g) )</tt><br>
<b>Default</b>: <tt>get(vertex_index,g)</tt><br>
</blockquote>
@ -201,21 +201,21 @@ IN <tt>EdgeIndexMap em</tt>
<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps edges from <tt>g</tt> to distinct integers in the range
</a> that maps edges from <tt>g</tt> to distinct integers in the range
<tt>[0, num_edges(g) )</tt><br>
<b>Default</b>: <tt>get(edge_index,g)</tt>, but this parameter is only used if
<b>Default</b>: <tt>get(edge_index,g)</tt>, but this parameter is only used if
the <tt>kuratowski_subgraph_iterator</tt> is provided.<br>
</blockquote>
<H3>Complexity</H3>
Assuming that both the vertex index and edge index supplied take time
<i>O(1)</i> to return an index and there are <i>O(n)</i>
total self-loops and parallel edges in the graph, most combinations of
arguments given to
<tt>boyer_myrvold_planarity_test</tt> result in an algorithm that runs in time
<i>O(n)</i> for a graph with <i>n</i> vertices and <i>m</i> edges. The only
exception is when Kuratowski subgraph isolation is requested for a dense graph
Assuming that both the vertex index and edge index supplied take time
<i>O(1)</i> to return an index and there are <i>O(n)</i>
total self-loops and parallel edges in the graph, most combinations of
arguments given to
<tt>boyer_myrvold_planarity_test</tt> result in an algorithm that runs in time
<i>O(n)</i> for a graph with <i>n</i> vertices and <i>m</i> edges. The only
exception is when Kuratowski subgraph isolation is requested for a dense graph
(a graph with <i>n = o(m)</i>) - the running time will be <i>O(n+m)</i>
<a href = "#2">[2]</a>.
@ -224,9 +224,9 @@ exception is when Kuratowski subgraph isolation is requested for a dense graph
<P>
<ul>
<li><a href="../example/simple_planarity_test.cpp">A simple planarity test</a>
<li><a href="../example/kuratowski_subgraph.cpp">Isolating a Kuratowski
<li><a href="../example/kuratowski_subgraph.cpp">Isolating a Kuratowski
Subgraph</a>
<li><a href="../example/straight_line_drawing.cpp">Using a planar embedding to
<li><a href="../example/straight_line_drawing.cpp">Using a planar embedding to
create a straight line drawing</a>
</ul>
@ -237,17 +237,17 @@ create a straight line drawing</a>
<h3>Notes</h3>
<p><a name="1">[1] A planar embedding is also called a <i>combinatorial
<p><a name="1">[1] A planar embedding is also called a <i>combinatorial
embedding</i>.
<p><a name="2">[2] The algorithm can still be made to run in time <i>O(n)</i>
for this case, if needed. <a href="planar_graphs.html#EulersFormula">Euler's
<p><a name="2">[2] The algorithm can still be made to run in time <i>O(n)</i>
for this case, if needed. <a href="planar_graphs.html#EulersFormula">Euler's
formula</a> implies that a planar graph with <i>n</i> vertices can have no more
than <i>3n - 6</i> edges, which means that any non-planar graph on <i>n</i>
vertices has a subgraph of only <i>3n - 5</i> edges that contains a Kuratowski
subgraph. So, if you need to find a Kuratowski subgraph of a graph with more
than <i>3n - 5</i> edges in time <i>O(n)</i>, you can create a subgraph of the
original graph consisting of any arbitrary <i>3n - 5</i> edges and pass that
than <i>3n - 6</i> edges, which means that any non-planar graph on <i>n</i>
vertices has a subgraph of only <i>3n - 5</i> edges that contains a Kuratowski
subgraph. So, if you need to find a Kuratowski subgraph of a graph with more
than <i>3n - 5</i> edges in time <i>O(n)</i>, you can create a subgraph of the
original graph consisting of any arbitrary <i>3n - 5</i> edges and pass that
graph to <tt>boyer_myrvold_planarity_test</tt>.
@ -256,4 +256,4 @@ graph to <tt>boyer_myrvold_planarity_test</tt>.
Copyright &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
aaron.windsor@gmail.com</a>)
</BODY>
</HTML>
</HTML>

78
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000, 2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Breadth-First Search</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -24,15 +24,15 @@
<PRE>
<i>// named parameter version</i>
template &lt;class Graph, class P, class T, class R&gt;
void breadth_first_search(Graph& G,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
void breadth_first_search(Graph& G,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
const bgl_named_params&lt;P, T, R&gt;&amp; params);
<i>// non-named parameter version</i>
template &lt;class Graph, class Buffer, class BFSVisitor,
template &lt;class Graph, class Buffer, class BFSVisitor,
class ColorMap&gt;
void breadth_first_search(const Graph&amp; g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
void breadth_first_search(const Graph&amp; g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
Buffer&amp; Q, BFSVisitor vis, ColorMap color);
</PRE>
@ -70,25 +70,25 @@ BFS algorithm is a listed below.
<pre>
BFS(<i>G</i>, <i>s</i>)
<b>for</b> each vertex <i>u in V[G]</i>
<i>color[u] :=</i> WHITE
<i>d[u] := infinity</i>
<i>p[u] := u</i>
<i>color[u] :=</i> WHITE
<i>d[u] := infinity</i>
<i>p[u] := u</i>
<b>end for</b>
<i>color[s] :=</i> GRAY
<i>d[s] := 0</i>
<i>color[s] :=</i> GRAY
<i>d[s] := 0</i>
ENQUEUE(<i>Q</i>, <i>s</i>)
<b>while</b> (<i>Q != &Oslash;</i>)
<b>while</b> (<i>Q != &Oslash;</i>)
<i>u :=</i> DEQUEUE(Q)
<b>for</b> each vertex <i>v in Adj[u]</i>
<b>if</b> (<i>color[v] =</i> WHITE)
<i>color[v] :=</i> GRAY
<i>d[v] := d[u] + 1</i>
<i>p[v] := u</i>
<i>color[v] :=</i> GRAY
<i>d[v] := d[u] + 1</i>
<i>p[v] := u</i>
ENQUEUE(<i>Q</i>, <i>v</i>)
<b>else</b>
<b>if</b> (<i>color[v] =</i> GRAY)
<b>if</b> (<i>color[v] =</i> GRAY)
...
<b>else</b>
<b>else</b>
...
<b>end for</b>
<i>color[u] :=</i> BLACK
@ -99,29 +99,29 @@ BFS(<i>G</i>, <i>s</i>)
<td valign="top">
<pre>
initialize vertex <i>u</i>
initialize vertex <i>u</i>
discover vertex <i>s</i>
discover vertex <i>s</i>
examine vertex <i>u</i>
examine vertex <i>u</i>
examine edge <i>(u,v)</i>
<i>(u,v)</i> is a tree edge
<i>(u,v)</i> is a tree edge
discover vertex <i>v</i>
discover vertex <i>v</i>
<i>(u,v)</i> is a non-tree edge
<i>(u,v)</i> has a gray target
<i>(u,v)</i> has a gray target
<i>(u,v)</i> has a black target
<i>(u,v)</i> has a black target
finish vertex <i>u</i>
finish vertex <i>u</i>
</pre>
</tr>
</table>
@ -244,7 +244,7 @@ UTIL: <tt>buffer(Buffer&amp; Q)</tt>
<b>Python</b>: The buffer must derive from the <a
href="./Buffer.html">Buffer</a> type for the graph.
</blockquote>
</blockquote>
<H3><A NAME="SECTION001330300000000000000">
@ -252,7 +252,7 @@ Complexity</A>
</H3>
<P>
The time complexity is <i>O(E + V)</i>.
The time complexity is <i>O(E + V)</i>.
<P>
@ -260,13 +260,13 @@ The time complexity is <i>O(E + V)</i>.
<ul>
<li><b><tt>vis.initialize_vertex(v, g)</tt></b> is invoked on every vertex
before the start of the search.
before the start of the search.
<li><b><tt>vis.examine_vertex(u, g)</tt></b>r is invoked in each
vertex as it is removed from the queue.
<li><b><tt>vis.examine_edge(e, g)</tt></b> is invoked on every out-edge
of each vertex immediately after the vertex is removed from the queue.
of each vertex immediately after the vertex is removed from the queue.
<li><b><tt>vis.tree_edge(e, g)</tt></b> is invoked (in addition to
<tt>examine_edge()</tt>) if the edge is a tree edge. The
@ -275,20 +275,20 @@ The time complexity is <i>O(E + V)</i>.
<li><b><tt>vis.discover_vertex(u, g)</tt></b> is invoked the first time the
algorithm encounters vertex <i>u</i>. All vertices closer to the
source vertex have been discovered, and vertices further from the
source have not yet been discovered.
source have not yet been discovered.
<li><b><tt>vis.non_tree_edge(e, g)</tt></b> is invoked (in addition to
<tt>examine_edge()</tt>) if the edge is not a tree edge.
<tt>examine_edge()</tt>) if the edge is not a tree edge.
<li><b><tt>vis.gray_target(e, g)</tt></b> is invoked (in addition to
<tt>non_tree_edge()</tt>) if the target vertex is colored gray at the
time of examination. The color gray indicates that
the vertex is currently in the queue.
the vertex is currently in the queue.
<li><b><tt>vis.black_target(e, g)</tt></b> is invoked (in addition to
<tt>non_tree_edge()</tt>) if the target vertex is colored black at the
time of examination. The color black indicates that the
vertex is no longer in the queue.
vertex is no longer in the queue.
<li><b><tt>vis.finish_vertex(u, g)</tt></b> is invoked after all of the out
edges of <i>u</i> have been examined and all of the adjacent vertices
@ -319,7 +319,7 @@ to <tt>listS</tt>.
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -335,4 +335,4 @@ to <tt>listS</tt>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

36
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000, 2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Breadth-First Visit</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -22,14 +22,14 @@
<P>
<PRE>
template &lt;class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class P, class T, class R&gt;
void breadth_first_visit(IncidenceGraph& G,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
void breadth_first_visit(IncidenceGraph& G,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
const bgl_named_params&lt;P, T, R&gt;&amp; params);
template &lt;class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./Buffer.html">Buffer</a>, class <a href="./BFSVisitor.html">BFSVisitor</a>, class ColorMap&gt;
void breadth_first_visit
(const IncidenceGraph&amp; g,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
(const IncidenceGraph&amp; g,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
Buffer&amp; Q, BFSVisitor vis, ColorMap color)
</PRE>
@ -110,7 +110,7 @@ UTIL: <tt>buffer(Buffer&amp; Q)</tt>
<b>Python</b>: The buffer must derive from the <a
href="./Buffer.html">Buffer</a> type for the graph.
</blockquote>
</blockquote>
<H3><A NAME="SECTION001330300000000000000">
@ -118,7 +118,7 @@ Complexity</A>
</H3>
<P>
The time complexity is <i>O(E)</i>.
The time complexity is <i>O(E)</i>.
<P>
@ -129,7 +129,7 @@ The time complexity is <i>O(E)</i>.
vertex as it is removed from the queue.
<li><b><tt>vis.examine_edge(e, g)</tt></b> is invoked on every out-edge
of each vertex immediately after the vertex is removed from the queue.
of each vertex immediately after the vertex is removed from the queue.
<li><b><tt>vis.tree_edge(e, g)</tt></b> is invoked (in addition to
<tt>examine_edge()</tt>) if the edge is a tree edge. The
@ -138,20 +138,20 @@ The time complexity is <i>O(E)</i>.
<li><b><tt>vis.discover_vertex(u, g)</tt></b> is invoked the first time the
algorithm encounters vertex <i>u</i>. All vertices closer to the
source vertex have been discovered, and vertices further from the
source have not yet been discovered.
source have not yet been discovered.
<li><b><tt>vis.non_tree_edge(e, g)</tt></b> is invoked (in addition to
<tt>examine_edge()</tt>) if the edge is not a tree edge.
<tt>examine_edge()</tt>) if the edge is not a tree edge.
<li><b><tt>vis.gray_target(e, g)</tt></b> is invoked (in addition to
<tt>non_tree_edge()</tt>) if the target vertex is colored gray at the
time of examination. The color gray indicates that
the vertex is currently in the queue.
the vertex is currently in the queue.
<li><b><tt>vis.black_target(e, g)</tt></b> is invoked (in addition to
<tt>non_tree_edge()</tt>) if the target vertex is colored black at the
time of examination. The color black indicates that the
vertex is no longer in the queue.
vertex is no longer in the queue.
<li><b><tt>vis.finish_vertex(u, g)</tt></b> is invoked after all of the out
edges of <i>u</i> have been examined and all of the adjacent vertices
@ -167,7 +167,7 @@ The time complexity is <i>O(E)</i>.
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -183,4 +183,4 @@ The time complexity is <i>O(E)</i>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

20
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Challenge</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -43,12 +43,12 @@ review. The pending items are:</li>
<li>Construct a set of planar graph algorithms.</li>
<ul>
<li> Is the graph planar?</li>
<li> &quot;Walk around the block&quot; and similar open and closed neighborhood
traversals. Note that edge traversals need to resolve to particular ends
<li> &quot;Walk around the block&quot; and similar open and closed neighborhood
traversals. Note that edge traversals need to resolve to particular ends
and sides (see below), not just to the edge as a whole.</li>
<li> Given a point, find the nearest vertex, edge, or bounded polygon.
<li> Given a point, find the nearest vertex, edge, or bounded polygon.
Again, edges are viewed as having left and right sides.</li>
<li> Given a line segment, find intersecting vertices, edges, or bounded
<li> Given a line segment, find intersecting vertices, edges, or bounded
polygons.</li>
<li> Given a polygon, find intersecting whatever...</li>
<li> Various minimum bounding rectangle and clipping problems.</li>
@ -117,4 +117,4 @@ It is currently difficult to use from a C++ program.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

8
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@ -1,14 +1,14 @@
<html><!--
Copyright (c) 2004 Trustees of Indiana University
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>Function template circle_graph_layout</title></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><table cellpadding="2" width="100%"><td valign="top"><img src="../../../boost.png" alt="boost.png (6897 bytes)" width="277" height="86"></td><td align="center"><a href="../../../index.htm">Home</a></td><td align="center"><a href="../../libraries.htm">Libraries</a></td><td align="center"><a href="http://www.boost.org/people/people.htm">People</a></td><td align="center"><a href="http://www.boost.org/more/faq.htm">FAQ</a></td><td align="center"><a href="../../../more/index.htm">More</a></td></table><hr><div class="refentry" lang="en"><a name="id103562-bb"></a><div class="titlepage"><div></div><div></div></div><div class="refnamediv"><h2><img src="figs/python.gif" alt="(Python)"/><span class="refentrytitle">Function template circle_graph_layout</span></h2><p>boost::circle_graph_layout &#8212; Layout the graph with the vertices at the points of a regular n-polygon. </p></div><h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2><div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis">
<span class="bold"><b>template</b></span>&lt;<span class="bold"><b>typename</b></span> VertexListGraph, <span class="bold"><b>typename</b></span> PositionMap, <span class="bold"><b>typename</b></span> Radius&gt;
  <span class="type"><span class="bold"><b>void</b></span></span> circle_graph_layout(<span class="bold"><b>const</b></span> VertexListGraph &amp; g, PositionMap position,
                           Radius radius);</pre></div><div class="refsect1" lang="en"><a name="id821794"></a><h2>Where Defined</h2><a href="../../../boost/graph/circle_layout.hpp">boost/graph/circle_layout.hpp</a><h2>Description</h2><p>The distance from the center of the polygon to each point is determined by the <tt class="computeroutput">radius</tt> parameter. The <tt class="computeroutput">position</tt> parameter must be an Lvalue Property Map whose value type is a class type containing <tt class="computeroutput">x</tt> and <tt class="computeroutput">y</tt> members that will be set to the <tt class="computeroutput">x</tt> and <tt class="computeroutput">y</tt> coordinates.
<span class="bold"><b>template</b></span>&lt;<span class="bold"><b>typename</b></span> VertexListGraph, <span class="bold"><b>typename</b></span> PositionMap, <span class="bold"><b>typename</b></span> Radius&gt;
  <span class="type"><span class="bold"><b>void</b></span></span> circle_graph_layout(<span class="bold"><b>const</b></span> VertexListGraph &amp; g, PositionMap position,
                           Radius radius);</pre></div><div class="refsect1" lang="en"><a name="id821794"></a><h2>Where Defined</h2><a href="../../../boost/graph/circle_layout.hpp">boost/graph/circle_layout.hpp</a><h2>Description</h2><p>The distance from the center of the polygon to each point is determined by the <tt class="computeroutput">radius</tt> parameter. The <tt class="computeroutput">position</tt> parameter must be an Lvalue Property Map whose value type is a class type containing <tt class="computeroutput">x</tt> and <tt class="computeroutput">y</tt> members that will be set to the <tt class="computeroutput">x</tt> and <tt class="computeroutput">y</tt> coordinates.
<h2>Parameters</h2>
IN: <tt>const VertexListGraph&amp; g</tt>

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48
doc/compressed_sparse_row.html
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@ -2,7 +2,7 @@
<html>
<!--
Copyright (c) 2005-2009 Trustees of Indiana University
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
@ -32,12 +32,12 @@ function address(host, user) {
</script>
</head>
<body>
<IMG SRC="../../../boost.png"
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86"></img>
<h1>Compressed Sparse Row Graph</h1>
<p>The class template <code>compressed_sparse_row_graph</code> is
a graph class that uses the compact Compressed Sparse Row (CSR)
format to store directed (and bidirectional) graphs. While CSR graphs have
@ -101,8 +101,8 @@ function address(host, user) {
<pre>
namespace boost {
template&lt;typename <a href="#Directed">Directed</a> = directedS, typename <a href="#VertexProperty">VertexProperty</a> = no_property,
typename <a href="#EdgeProperty">EdgeProperty</a> = no_property, typename <a href="#GraphProperty">GraphProperty</a> = no_property,
template&lt;typename <a href="#Directed">Directed</a> = directedS, typename <a href="#VertexProperty">VertexProperty</a> = no_property,
typename <a href="#EdgeProperty">EdgeProperty</a> = no_property, typename <a href="#GraphProperty">GraphProperty</a> = no_property,
typename <a href="#Vertex">Vertex</a> = std::size_t, typename <a href="#EdgeIndex">EdgeIndex</a> = Vertex&gt;
class compressed_sparse_row_graph
{
@ -173,7 +173,7 @@ public:
template&lt;typename Graph, typename VertexIndexMap&gt;
<a href="#graph-const">compressed_sparse_row_graph</a>(const Graph&amp; g, const VertexIndexMap&amp; vi,
vertices_size_type numverts,
edges_size_type numedges);
edges_size_type numedges);
template&lt;typename Graph, typename VertexIndexMap&gt;
compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi);
@ -202,17 +202,17 @@ public:
<i>// <a href="IncidenceGraph.html">Incidence Graph requirements</a></i>
vertex_descriptor source(edge_descriptor, const compressed_sparse_row_graph&amp;);
vertex_descriptor target(edge_descriptor, const compressed_sparse_row_graph&amp;);
std::pair&lt;out_edge_iterator, out_edge_iterator&gt;
std::pair&lt;out_edge_iterator, out_edge_iterator&gt;
out_edges(vertex_descriptor, const compressed_sparse_row_graph&amp;);
degree_size_type out_degree(vertex_descriptor v, const compressed_sparse_row_graph&amp;);
<i>// <a href="BidirectionalGraph.html">Bidirectional Graph requirements <b>(bidirectional only)</b></a></i>
std::pair&lt;in_edge_iterator, in_edge_iterator&gt;
std::pair&lt;in_edge_iterator, in_edge_iterator&gt;
in_edges(vertex_descriptor, const compressed_sparse_row_graph&amp;);
degree_size_type in_degree(vertex_descriptor v, const compressed_sparse_row_graph&amp;);
<i>// <a href="AdjacencyGraph.html">Adjacency Graph requirements</a></i>
std::pair&lt;adjacency_iterator, adjacency_iterator&gt;
std::pair&lt;adjacency_iterator, adjacency_iterator&gt;
adjacent_vertices(vertex_descriptor, const compressed_sparse_row_graph&amp;);
<i>// <a href="VertexListGraph.html">Vertex List Graph requirements</a></i>
@ -227,7 +227,7 @@ edges_size_type num_edges(const compressed_sparse_row_graph&amp;);
vertex_descriptor <a href="#vertex-lookup">vertex</a>(vertices_size_type i, const compressed_sparse_row_graph&amp;);
<i>// <a href="#edge-access">Edge access</a></i>
std::pair&lt;edge_descriptor, bool&gt;
std::pair&lt;edge_descriptor, bool&gt;
<a href="#edge">edge</a>(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
edge_descriptor <a href="#edge_from_index">edge_from_index</a>(edges_size_type i, const compressed_sparse_row_graph&amp;);
@ -283,7 +283,7 @@ void <a href="#add_edges_sorted_prop">add_edges_sorted</a>(BidirectionalIterator
<p><code>&lt;<a href="../../../boost/graph/compressed_sparse_row_graph.hpp">boost/graph/compressed_sparse_row_graph.hpp</a>&gt;</code></p>
<a name="models"></a><h2>Models</h2>
<p>The <tt>compressed_sparse_row_graph</tt> class template models
(i.e., implements the requirements of) many of the
BGL <a href="graph_concepts.html">graph concepts</a>, allowing it
@ -628,7 +628,7 @@ void <a href="#add_edges_sorted_prop">add_edges_sorted</a>(BidirectionalIterator
template&lt;typename Graph, typename VertexIndexMap&gt;
compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi,
vertices_size_type numverts,
edges_size_type numedges);
edges_size_type numedges);
template&lt;typename Graph, typename VertexIndexMap&gt;
compressed_sparse_row_graph(const Graph&amp; g, const VertexIndexMap&amp; vi);
@ -666,14 +666,14 @@ void <a href="#add_edges_sorted_prop">add_edges_sorted</a>(BidirectionalIterator
<ul>
<li><tt>g</tt>: The incoming graph.</li>
<li><tt>vi</tt>: A map from vertices to indices. If not
provided, <tt>get(vertex_index, g)</tt> will be used.</li>
<li><tt>numverts</tt>: The number of vertices in the graph
<tt>g</tt>. If not provided, <tt>Graph</tt> must be a model of
<a href="VertexListGraph.html">VertexListGraph</a>.</li>
<li><tt>numedges</tt>: The number of edges in the graph
<tt>g</tt>. If not provided, <tt>Graph</tt> must be a model of
<a href="EdgeListGraph.html">EdgeListGraph</a>.</li>
@ -726,7 +726,7 @@ void <a href="#add_edges_sorted_prop">add_edges_sorted</a>(BidirectionalIterator
<a name="edge-access"></a><h3>Edge access</h3>
<pre><a name="edge"></a>
std::pair&lt;edge_descriptor, bool&gt;
std::pair&lt;edge_descriptor, bool&gt;
edge(vertex_descriptor u, vertex_descriptor v, const compressed_sparse_row_graph&amp;);
</pre>
@ -766,7 +766,7 @@ template&lt;typename <a href="./PropertyTag.html">PropertyTag</a>&gt;
property_map&lt;compressed_sparse_row_graph, Tag&gt;::const_type
get(PropertyTag, const compressed_sparse_row_graph&amp; g)
</pre>
<p class="indent">
Returns the property map object for the vertex property
specified by <TT>PropertyTag</TT>. The <TT>PropertyTag</TT> must
@ -816,7 +816,7 @@ get_property(const compressed_sparse_row_graph&amp; g, GraphPropertyTag);
<p class="indent">
Return the property specified by <tt>GraphPropertyTag</tt> that
is attached to the graph object <tt>g</tt>.
is attached to the graph object <tt>g</tt>.
</p>
<hr></hr>
@ -840,7 +840,7 @@ void set_property(const compressed_sparse_row_graph&amp; g, GraphPropertyTag,
template&lt;typename InputIterator&gt;
void add_edges(InputIterator first, InputIterator last, compressed_sparse_row_graph&amp; g)
</pre>
<p class="indent">
Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
The <tt>InputIterator</tt> must be a model of <a
@ -856,7 +856,7 @@ void add_edges(InputIterator first, InputIterator last, compressed_sparse_row_gr
template&lt;typename InputIterator, typename EPIter&gt;
void add_edges(InputIterator first, InputIterator last, EPIter ep_first, EPIter ep_last, compressed_sparse_row_graph&amp; g)
</pre>
<p class="indent">
Add a range of edges (from <tt>first</tt> to <tt>last</tt>) with
corresponding edge properties (from <tt>ep_first</tt> to
@ -876,7 +876,7 @@ void add_edges(InputIterator first, InputIterator last, EPIter ep_first, EPIter
template&lt;typename BidirectionalIterator&gt;
void add_edges_sorted(BidirectionalIterator first, BidirectionalIterator last, compressed_sparse_row_graph&amp; g)
</pre>
<p class="indent">
Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
The <tt>BidirectionalIterator</tt> must be a model of <a
@ -893,7 +893,7 @@ void add_edges_sorted(BidirectionalIterator first, BidirectionalIterator last, c
template&lt;typename BidirectionalIterator, typename EPIter&gt;
void add_edges_sorted(BidirectionalIterator first, BidirectionalIterator last, EPIter ep_iter, compressed_sparse_row_graph&amp; g)
</pre>
<p class="indent">
Add a range of edges (from <tt>first</tt> to <tt>last</tt>) to the graph.
The <tt>BidirectionalIterator</tt> and <tt>EPIter</tt> must be models of
@ -950,7 +950,7 @@ BGL_FORALL_VERTICES(v, g, WebGraph)
// Output each of the links
std::cout &lt;&lt; "The web graph:" &lt;&lt; std::endl;
BGL_FORALL_EDGES(e, g, WebGraph)
std::cout &lt;&lt; " " &lt;&lt; g[source(e, g)].url &lt;&lt; " -> " &lt;&lt; g[target(e, g)].url
std::cout &lt;&lt; " " &lt;&lt; g[source(e, g)].url &lt;&lt; " -> " &lt;&lt; g[target(e, g)].url
&lt;&lt; std::endl;
</pre>

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000-2001
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Connected Components</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -154,4 +154,4 @@ undirected graph.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

26
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Constructing Graph Algorithms</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -113,7 +113,7 @@ color of all the vertices to "uncolored."
namespace boost {
template &lt;class VertexListGraph, class Order, class Color&gt;
typename graph_traits&lt;VertexListGraph&gt;::vertices_size_type
sequential_vertex_color_ting(const VertexListGraph&amp; G,
sequential_vertex_color_ting(const VertexListGraph&amp; G,
Order order, Color color)
{
typedef graph_traits&lt;VertexListGraph&gt; GraphTraits;
@ -127,27 +127,27 @@ namespace boost {
BOOST_CONCEPT_ASSERT(( IntegerConcept&lt;ColorType&gt; ));
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept&lt;Order, size_type&gt; ));
BOOST_STATIC_ASSERT((is_same&lt;OrderType, vertex_descriptor&gt;::value));
size_type max_color = 0;
const size_type V = num_vertices(G);
std::vector&lt;size_type&gt;
std::vector&lt;size_type&gt;
mark(V, numeric_limits_max(max_color));
typename GraphTraits::vertex_iterator v, vend;
for (boost::tie(v, vend) = vertices(G); v != vend; ++v)
color[*v] = V - 1; // which means "not colored"
for (size_type i = 0; i &lt; V; i++) {
vertex_descriptor current = order[i];
// mark all the colors of the adjacent vertices
typename GraphTraits::adjacency_iterator ai, aend;
for (boost::tie(ai, aend) = adjacent_vertices(current, G); ai != aend; ++ai)
mark[color[*ai]] = i;
mark[color[*ai]] = i;
// find the smallest color unused by the adjacent vertices
size_type smallest_color = 0;
while (smallest_color &lt; max_color &amp;&amp; mark[smallest_color] == i)
while (smallest_color &lt; max_color &amp;&amp; mark[smallest_color] == i)
++smallest_color;
// if all the colors are used up, increase the number of colors
@ -180,4 +180,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
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@ -1,24 +1,24 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Copy Graph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
<H1><TT>copy_graph</TT></H1>
<PRE>
template &lt;class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./MutableGraph.html">MutableGraph</a>&gt;
template &lt;class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./MutableGraph.html">MutableGraph</a>&gt;
void copy_graph(const VertexListGraph&amp; G, MutableGraph&amp; G_copy,
const bgl_named_params&lt;P, T, R&gt;&amp; params = <i>all defaults</i>)
</PRE>
@ -113,4 +113,4 @@ The time complexity is <i>O(V + E)</i>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,19 +1,19 @@
<HTML>
<!-- Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Head>
<Title>Boost Graph Library: Cuthill-Mckee Ordering</Title>
</Head>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -46,25 +46,25 @@
OutputIterator
cuthill_mckee_ordering(const IncidenceGraph&amp; g,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
OutputIterator inverse_permutation,
OutputIterator inverse_permutation,
ColorMap color, DegreeMap degree)
(2)
template &lt;class VertexListGraph, class OutputIterator&gt;
OutputIterator
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation);
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation);
template &lt;class VertexListGraph, class OutputIterator, class VertexIndexMap&gt;
OutputIterator
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation,
VertexIndexMap index_map);
template &lt;class VertexListGraph, class OutputIterator,
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation,
VertexIndexMap index_map);
template &lt;class VertexListGraph, class OutputIterator,
class ColorMap, class DegreeMap&gt;
OutputIterator
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation,
cuthill_mckee_ordering(const VertexListGraph&amp; g, OutputIterator inverse_permutation,
ColorMap color, DegreeMap degree)
(3)
template &lt;class IncidenceGraph, class OutputIterator,
class ColorMap, class DegreeMap&gt;
@ -72,7 +72,7 @@
cuthill_mckee_ordering(const IncidenceGraph&amp; g,
std::deque&lt; typename
graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor &gt; vertex_queue,
OutputIterator inverse_permutation,
OutputIterator inverse_permutation,
ColorMap color, DegreeMap degree)
</pre>
@ -92,10 +92,10 @@ increasing degree.
<p>
Version 1 of the algorithm lets the user choose the ``starting
vertex'', version 2 finds a good starting vertex using the
pseudo-peripheral pair heuristic (among each component), while version 3
contains the starting nodes for each vertex in the deque. The choice of the
``starting vertex'' can have a significant effect on the quality of the
ordering. For versions 2 and 3, <tt>find_starting_vertex</tt> will be called
pseudo-peripheral pair heuristic (among each component), while version 3
contains the starting nodes for each vertex in the deque. The choice of the
``starting vertex'' can have a significant effect on the quality of the
ordering. For versions 2 and 3, <tt>find_starting_vertex</tt> will be called
for each component in the graph, increasing run time significantly.
</p>
@ -140,7 +140,7 @@ For version 1:
<ul>
<li> <tt>IncidenceGraph&amp; g</tt> &nbsp;(IN) <br>
<li> <tt>IncidenceGraph&amp; g</tt> &nbsp;(IN) <br>
An undirected graph. The graph's type must be a model of <a
href="./IncidenceGraph.html">IncidenceGraph</a>.<br>
<b>Python</b>: The parameter is named <tt>graph</tt>.
@ -149,13 +149,13 @@ For version 1:
The starting vertex.<br>
<b>Python</b>: Unsupported parameter.
<li> <tt>OutputIterator inverse_permutation</tt> &nbsp(OUT) <br>
<li> <tt>OutputIterator inverse_permutation</tt> &nbsp(OUT) <br>
The new vertex ordering. The vertices are written to the <a
href="http://www.boost.org/sgi/stl/OutputIterator.html">output
iterator</a> in their new order.<br>
<b>Python</b>: This parameter is unused in Python. The new vertex
ordering is returned as a Python <tt>list</tt>.
<li> <tt>ColorMap color_map</tt> &nbsp(WORK) <br>
Used internally to keep track of the progress of the algorithm
(to avoid visiting the same vertex twice).<br>
@ -171,13 +171,13 @@ For version 2:
<ul>
<li> <tt>VertexListGraph&amp; g</tt> &nbsp;(IN) <br>
<li> <tt>VertexListGraph&amp; g</tt> &nbsp;(IN) <br>
An undirected graph. The graph's type must be a model of <a
href="./VertexListGraph.html">VertexListGraph</a> and <a href="./IncidenceGraph.html">IncidenceGraph</a>.<br>
<b>Python</b>: The parameter is named <tt>graph</tt>.
<li> <tt><a href="http://www.boost.org/sgi/stl/OutputIterator.html">
OutputIterator</a> inverse_permutation</tt> &nbsp(OUT) <br>
OutputIterator</a> inverse_permutation</tt> &nbsp(OUT) <br>
The new vertex ordering. The vertices are written to the
output iterator in their new order.<br>
<b>Python</b>: This parameter is unused in Python. The new vertex
@ -198,7 +198,7 @@ For version 3:
<ul>
<li> <tt>IncidenceGraph&amp; g</tt> &nbsp;(IN) <br>
<li> <tt>IncidenceGraph&amp; g</tt> &nbsp;(IN) <br>
An undirected graph. The graph's type must be a model of <a
href="./IncidenceGraph.html">IncidenceGraph</a>.<br>
<b>Python</b>: The parameter is named <tt>graph</tt>.
@ -207,13 +207,13 @@ For version 3:
The deque containing the starting vertices for each component.<br>
<b>Python</b>: Unsupported parameter.
<li> <tt>OutputIterator inverse_permutation</tt> &nbsp(OUT) <br>
<li> <tt>OutputIterator inverse_permutation</tt> &nbsp(OUT) <br>
The new vertex ordering. The vertices are written to the <a
href="http://www.boost.org/sgi/stl/OutputIterator.html">output
iterator</a> in their new order.<br>
<b>Python</b>: This parameter is unused in Python. The new vertex
ordering is returned as a Python <tt>list</tt>.
<li> <tt>ColorMap color_map</tt> &nbsp(WORK) <br>
Used internally to keep track of the progress of the algorithm
(to avoid visiting the same vertex twice).<br>
@ -245,4 +245,4 @@ and <tt>degree_property_map</tt> in <tt>boost/graph/properties.hpp</tt>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Piotr Wygocki 2013
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Cycle Canceling for Min Cost Max Flow</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -23,25 +23,25 @@
<i>// named parameter version</i>
template &lt;class <a href="./Graph.html">Graph</a>, class P, class T, class R&gt;
void cycle_canceling(
Graph &amp;g,
Graph &amp;g,
const bgl_named_params&lt;P, T, R&gt; &amp; params = <i>all defaults</i>)
<i>// non-named parameter version</i>
template &lt;class <a href="./Graph.html">Graph</a>, class Pred, class Distance, class Reversed, class ResidualCapacity, class Weight&gt;
void cycle_canceling(const Graph &amp; g, Weight weight, Reversed rev, ResidualCapacity residual_capacity, Pred pred, Distance distance)
void cycle_canceling(const Graph &amp; g, Weight weight, Reversed rev, ResidualCapacity residual_capacity, Pred pred, Distance distance)
</PRE>
<P>
The <tt>cycle_canceling()</tt> function calculates the minimum cost flow of a network with given flow. See Section <a
href="./graph_theory_review.html#sec:network-flow-algorithms">Network
Flow Algorithms</a> for a description of maximum flow.
Flow Algorithms</a> for a description of maximum flow.
For given flow values <i> f(u,v)</i> function minimizes flow cost in such a way, that for each <i>v in V</i> the
<i> sum<sub> u in V</sub> f(v,u) </i> is preserved. Particularly if the input flow was the maximum flow, the function produces min cost max flow.
The function calculates the flow values <i>f(u,v)</i> for all <i>(u,v)</i> in
<i>E</i>, which are returned in the form of the residual capacity
<i>r(u,v) = c(u,v) - f(u,v)</i>.
<i>r(u,v) = c(u,v) - f(u,v)</i>.
<p>
There are several special requirements on the input graph and property
@ -51,12 +51,12 @@ include the reverse edge for every edge in <i>E</i>. That is, the
input graph should be <i>G<sub>in</sub> = (V,{E U
E<sup>T</sup>})</i>. The <tt>ReverseEdgeMap</tt> argument <tt>rev</tt>
must map each edge in the original graph to its reverse edge, that is
<i>(u,v) -> (v,u)</i> for all <i>(u,v)</i> in <i>E</i>.
<i>(u,v) -> (v,u)</i> for all <i>(u,v)</i> in <i>E</i>.
The <tt>WeightMap</tt> has to map each edge from <i>E<sup>T</sup></i> to <i>-weight</i> of its reversed edge.
Note that edges from <i>E</i> can have negative weights.
Note that edges from <i>E</i> can have negative weights.
<p>
If weights in the graph are nonnegative, the
<a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a>
If weights in the graph are nonnegative, the
<a href="./successive_shortest_path_nonnegative_weights.html"><tt>successive_shortest_path_nonnegative_weights()</tt></a>
might be better choice for min cost max flow.
<p>
@ -70,7 +70,7 @@ If there is no negative cycle in the network, the cost is optimized.
<p>
Note that, although we mention capacity in the problem description, the actual algorithm doesn't have to now it.
<p>
<p>
In order to find the cost of the result flow use:
<a href="./find_flow_cost.html"><tt>find_flow_cost()</tt></a>.
@ -92,10 +92,10 @@ IN: <tt>Graph&amp; g</tt>
<i>(u,v)</i> in the graph, the reverse edge <i>(v,u)</i> must also
be in the graph.
</blockquote>
<h3>Named Parameters</h3>
IN/OUT: <tt>residual_capacity_map(ResidualCapacityEdgeMap res)</tt>
<blockquote>
This maps edges to their residual capacity. The type must be a model
@ -142,7 +142,7 @@ UTIL: <tt>predecessor_map(PredEdgeMap pred)</tt>
using the <tt>i_map</tt> for the index map.
</blockquote>
UTIL: <tt>distance_map(DistanceMap d_map)</tt>
UTIL: <tt>distance_map(DistanceMap d_map)</tt>
<blockquote>
The shortest path weight from the source vertex <tt>s</tt> to each
vertex in the graph <tt>g</tt> is recorded in this property map. The
@ -150,7 +150,7 @@ UTIL: <tt>distance_map(DistanceMap d_map)</tt>
shortest path. The type <tt>DistanceMap</tt> must be a model of <a
href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
Property Map</a>. The vertex descriptor type of the graph needs to
be usable as the key type of the distance map.
be usable as the key type of the distance map.
<b>Default:</b> <a
href="../../property_map/doc/iterator_property_map.html">
@ -178,8 +178,8 @@ IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
</blockquote>
<h3>Complexity</h3>
In the integer capacity and weight case, if <i>C</i> is the initial cost of the flow, then the complexity is <i> O(C * |V| * |E|)</i>,
where <i>O(|E|* |V|)</i> is the complexity of the bellman ford shortest paths algorithm and <i>C</i> is upper bound on number of iteration.
In the integer capacity and weight case, if <i>C</i> is the initial cost of the flow, then the complexity is <i> O(C * |V| * |E|)</i>,
where <i>O(|E|* |V|)</i> is the complexity of the bellman ford shortest paths algorithm and <i>C</i> is upper bound on number of iteration.
In many real world cases number of iterations is much smaller than <i>C</i>.
@ -203,7 +203,7 @@ Piotr Wygocki, University of Warsaw (<A HREF="mailto:wygos@mimuw.edu.pl">wygos a
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>
<!-- LocalWords: HTML Siek Edmonds BGCOLOR ffffff ee VLINK ALINK ff IMG SRC
-->
<!-- LocalWords: gif ALT BR sec edmonds karp TT DIV CELLPADDING TR TD PRE lt

70
doc/dag_shortest_paths.html
View File

@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Directed Acyclic Graph Shortest Paths</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -30,21 +30,21 @@ void dag_shortest_paths(const VertexListGraph&amp; g,
const bgl_named_params&lt;Param,Tag,Rest&gt;&amp; params)
<i>// non-named parameter version</i>
template &lt;class VertexListGraph, class DijkstraVisitor,
class DistanceMap, class WeightMap, class ColorMap,
template &lt;class VertexListGraph, class DijkstraVisitor,
class DistanceMap, class WeightMap, class ColorMap,
class PredecessorMap,
class Compare, class Combine,
class Compare, class Combine,
class DistInf, class DistZero&gt;
void dag_shortest_paths(const VertexListGraph&amp; g,
typename graph_traits&lt;VertexListGraph&gt;::vertex_descriptor s,
typename graph_traits&lt;VertexListGraph&gt;::vertex_descriptor s,
DistanceMap distance, WeightMap weight, ColorMap color,
PredecessorMap pred, DijkstraVisitor vis,
PredecessorMap pred, DijkstraVisitor vis,
Compare compare, Combine combine, DistInf inf, DistZero zero)
</PRE>
<P>
This algorithm&nbsp;[<A HREF="bibliography.html#clr90">8</A>] solves
the single-source shortest-paths problem on a weighted, directed
the single-source shortest-paths problem on a weighted, directed
acyclic graph (DAG). This algorithm is more efficient for DAG's
than either the Dijkstra or Bellman-Ford algorithm.
Use breadth-first search instead of this algorithm
@ -74,7 +74,7 @@ algorithm's event points.</P>
<h3>Parameters</h3>
IN: <tt>const VertexListGraph&amp; g</tt>
IN: <tt>const VertexListGraph&amp; g</tt>
<blockquote>
The graph object on which the algorithm will be applied.
The type <tt>VertexListGraph</tt> must be a model of \concept{VertexListGraph}.<br>
@ -82,7 +82,7 @@ IN: <tt>const VertexListGraph&amp; g</tt>
<b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>
IN: <tt>vertex_descriptor s</tt>
IN: <tt>vertex_descriptor s</tt>
<blockquote>
The source vertex. All distance will be calculated from this vertex,
and the shortest paths tree will be rooted at this vertex.<br>
@ -92,7 +92,7 @@ IN: <tt>vertex_descriptor s</tt>
<h3>Named Parameters</h3>
IN: <tt>weight_map(WeightMap w_map)</tt>
IN: <tt>weight_map(WeightMap w_map)</tt>
<blockquote>
The weight or ``length'' of each edge in the graph.
The type <tt>WeightMap</tt> must be a model of
@ -106,7 +106,7 @@ IN: <tt>weight_map(WeightMap w_map)</tt>
</blockquote>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(g))</tt>. This is necessary for efficient updates of the
@ -124,7 +124,7 @@ IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<blockquote>
The predecessor map records the edges in the minimum spanning
tree. Upon completion of the algorithm, the edges <i>(p[u],u)</i>
@ -139,7 +139,7 @@ OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<b>Python</b>: Must be a <tt>vertex_vertex_map</tt> for the graph.<br>
</blockquote>
UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
<blockquote>
The shortest path weight from the source vertex <tt>s</tt> to each
vertex in the graph <tt>g</tt> is recorded in this property map. The
@ -147,7 +147,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
shortest path. The type <tt>DistanceMap</tt> must be a model of <a
href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
Property Map</a>. The vertex descriptor type of the graph needs to
be usable as the key type of the distance map.
be usable as the key type of the distance map.
The value type of the distance map is the element type of a <a
href="./Monoid.html">Monoid</tt> formed with the <tt>combine</tt>
@ -166,7 +166,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
<b>Python</b>: Must be a <tt>vertex_double_map</tt> for the graph.
</blockquote>
IN: <tt>distance_compare(CompareFunction cmp)</tt>
IN: <tt>distance_compare(CompareFunction cmp)</tt>
<blockquote>
This function is use to compare distances to determine which vertex
is closer to the source vertex. The <tt>CompareFunction</tt> type
@ -182,7 +182,7 @@ IN: <tt>distance_compare(CompareFunction cmp)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_combine(CombineFunction cmb)</tt>
IN: <tt>distance_combine(CombineFunction cmb)</tt>
<blockquote>
This function is used to combine distances to compute the distance
of a path. The <tt>CombineFunction</tt> type must be a model of <a
@ -199,7 +199,7 @@ IN: <tt>distance_combine(CombineFunction cmb)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_inf(D inf)</tt>
IN: <tt>distance_inf(D inf)</tt>
<blockquote>
The <tt>inf</tt> object must be the greatest value of any <tt>D</tt> object.
That is, <tt>compare(d, inf) == true</tt> for any <tt>d != inf</tt>.
@ -209,7 +209,7 @@ IN: <tt>distance_inf(D inf)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_zero(D zero)</tt>
IN: <tt>distance_zero(D zero)</tt>
<blockquote>
The <tt>zero</tt> value must be the identity element for the
<a href="./Monoid.html">Monoid</a> formed by the distance values
@ -220,7 +220,7 @@ IN: <tt>distance_zero(D zero)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
<blockquote>
This is used during the execution of the algorithm to mark the
vertices. The vertices start out white and become gray when they are
@ -242,13 +242,13 @@ UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
the graph.
</blockquote>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
<blockquote>
Use this to specify actions that you would like to happen
during certain event points within the algorithm.
The type <tt>DijkstraVisitor</tt> must be a model of the
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
The visitor object is passed by value <a
href="#1">[1]</a>.<br>
<b>Default:</b> <tt>dijkstra_visitor&lt;null_visitor&gt;</tt><br>
@ -272,21 +272,21 @@ The time complexity is <i>O(V + E)</i>.
is invoked on each vertex in the graph before the start of the
algorithm.
<li><b><tt>vis.examine_vertex(u, g)</tt></b>
is invoked on a vertex as it is added to set <i>S</i>.
is invoked on a vertex as it is added to set <i>S</i>.
At this point we know that <i>(p[u],u)</i>
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
of the examined vertices is monotonically increasing
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<li><b><tt>vis.examine_edge(e, g)</tt></b>
is invoked on each out-edge of a vertex immediately after it has
been added to set <i>S</i>.
been added to set <i>S</i>.
<li><b><tt>vis.edge_relaxed(e, g)</tt></b>
is invoked on edge <i>(u,v)</i> if <i>d[u] + w(u,v) < d[v]</i>.
The edge <i>(u,v)</i> that participated in the last
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
<li><b><tt>vis.discover_vertex(v, g)</tt></b>
is invoked on vertex <i>v</i> when the edge
is invoked on vertex <i>v</i> when the edge
<i>(u,v)</i> is examined and <i>v</i> is WHITE. Since
a vertex is colored GRAY when it is discovered,
each reacable vertex is discovered exactly once.
@ -306,7 +306,7 @@ algorithm.
<H3>Notes</H3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -322,5 +322,5 @@ algorithm.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

50
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Depth-First Search</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -31,7 +31,7 @@ template &lt;class Graph, class <a href="DFSVisitor.html">DFSVisitor</a>, class
void depth_first_search(const Graph&amp; g, DFSVisitor vis, ColorMap color)
template &lt;class Graph, class <a href="DFSVisitor.html">DFSVisitor</a>, class ColorMap&gt;
void depth_first_search(const Graph&amp; g, DFSVisitor vis, ColorMap color,
void depth_first_search(const Graph&amp; g, DFSVisitor vis, ColorMap color,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start)
</PRE>
@ -84,33 +84,33 @@ be used to do this.
<td valign="top">
<pre>
DFS(<i>G</i>)
<b>for</b> each vertex <i>u in V</i>
<b>for</b> each vertex <i>u in V</i>
<i>color[u] :=</i> WHITE
<i>p[u] = u</i>
<i>p[u] = u</i>
<b>end for</b>
<i>time := 0</i>
<b>if</b> there is a starting vertex <i>s</i>
<b>call</b> DFS-VISIT(<i>G</i>, <i>s</i>)
<b>for</b> each vertex <i>u in V</i>
<b>for</b> each vertex <i>u in V</i>
<b>if</b> <i>color[u] =</i> WHITE
<b>call</b> DFS-VISIT(<i>G</i>, <i>u</i>)
<b>end for</b>
return (<i>p</i>,<i>d_time</i>,<i>f_time</i>) <br>
DFS-VISIT(<i>G</i>, <i>u</i>)
DFS-VISIT(<i>G</i>, <i>u</i>)
<i>color[u] :=</i> GRAY
<i>d_time[u] := time := time + 1</i>
<b>for</b> each <i>v in Adj[u]</i>
<i>d_time[u] := time := time + 1</i>
<b>for</b> each <i>v in Adj[u]</i>
<b>if</b> (<i>color[v] =</i> WHITE)
<i>p[v] = u</i>
<i>p[v] = u</i>
<b>call</b> DFS-VISIT(<i>G</i>, <i>v</i>)
<b>else if</b> (<i>color[v] =</i> GRAY)
<b>else if</b> (<i>color[v] =</i> GRAY)
<i>...</i>
<b>else if</b> (<i>color[v] =</i> BLACK)
<b>else if</b> (<i>color[v] =</i> BLACK)
<i>...</i>
<i>...</i>
<b>end for</b>
<i>color[u] :=</i> BLACK
<i>f_time[u] := time := time + 1</i>
<i>f_time[u] := time := time + 1</i>
<pre>
</td>
<td valign="top">
@ -252,27 +252,27 @@ The time complexity is <i>O(E + V)</i>.
<li><b><tt>vis.start_vertex(s, g)</tt></b> is invoked on the source
vertex once before the start of the search.
<li><b><tt>vis.discover_vertex(u, g)</tt></b> is invoked when a vertex
is encountered for the first time.
<li><b><tt>vis.examine_edge(e, g)</tt></b> is invoked on every out-edge
of each vertex after it is discovered.
<li><b><tt>vis.tree_edge(e, g)</tt></b> is invoked on each edge as it
becomes a member of the edges that form the search tree. If you
wish to record predecessors, do so at this event point.
<li><b><tt>vis.back_edge(e, g)</tt></b> is invoked on the back edges in
the graph.
<li><b><tt>vis.forward_or_cross_edge(e, g)</tt></b> is invoked on
forward or cross edges in the graph. In an undirected graph this
method is never called.
<li><b><tt>vis.finish_edge(e, g)</tt></b> is invoked on the non-tree edges in
the graph as well as on each tree edge after its target vertex is finished.
<li><b><tt>vis.finish_edge(e, g)</tt></b> is invoked on the non-tree edges in
the graph as well as on each tree edge after its target vertex is finished.
<li><b><tt>vis.finish_vertex(u, g)</tt></b> is invoked on a vertex after
all of its out edges have been added to the search tree and all of
the adjacent vertices have been discovered (but before their
@ -295,7 +295,7 @@ The example in <a href="../example/dfs-example.cpp">
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -317,4 +317,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

22
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View File

@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Depth-First Visit</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -25,13 +25,13 @@
<PRE>
template &lt;class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>, class ColorMap&gt;
void depth_first_visit(IncidenceGraph& g,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
DFSVisitor&amp; vis, ColorMap color)
template &lt;class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>, class ColorMap,
template &lt;class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>, class ColorMap,
class TerminatorFunc&gt;
void depth_first_visit(IncidenceGraph& g,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
typename graph_traits&lt;IncidenceGraph&gt;::vertex_descriptor s,
DFSVisitor&amp; vis, ColorMap color, TerminatorFunc func = TerminatorFunc())
</PRE>
@ -41,7 +41,7 @@ component as the source vertex <tt>s</tt>, using the <a
href="./graph_theory_review.html#sec:dfs-algorithm">depth-first
pattern</a>. The main purpose of the function is for the
implementation of <TT>depth_first_search()</TT> though sometimes it is
useful on its own.
useful on its own.
<p>
The <tt>DFSVisitor</tt> supplied by the user determines what
@ -124,7 +124,7 @@ Time complexity is <i>O(E)</i>.
<h3>Notes</h3>
<p><a name="1">[1]</a>
<p><a name="1">[1]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -141,4 +141,4 @@ Time complexity is <i>O(E)</i>.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: dfs_visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -108,4 +108,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Dijkstra's Shortest Paths</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -29,14 +29,14 @@ dijkstra_shortest_paths(Graph&amp; g,
const bgl_named_params&lt;P, T, R&gt;&amp; params);
<i>// non-named parameter version</i>
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
typename PredecessorMap, typename DistanceMap,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">CompareFunction</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">CombineFunction</a>,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">CompareFunction</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">CombineFunction</a>,
typename DistInf, typename DistZero, typename ColorMap = <i>default</i>&gt;
void dijkstra_shortest_paths
(const Graph&amp; g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
PredecessorMap predecessor, DistanceMap distance, WeightMap weight,
typename graph_traits&lt;Graph&gt;::vertex_descriptor s,
PredecessorMap predecessor, DistanceMap distance, WeightMap weight,
VertexIndexMap index_map,
CompareFunction compare, CombineFunction combine, DistInf inf, DistZero zero,
DijkstraVisitor vis, ColorMap color = <i>default</i>)
@ -123,12 +123,12 @@ indicated by the labels on the right.
<pre>
DIJKSTRA(<i>G</i>, <i>s</i>, <i>w</i>)
<b>for</b> each vertex <i>u in V</i> <b>(This loop is not run in dijkstra_shortest_paths_no_init)</b>
<i>d[u] := infinity</i>
<i>p[u] := u</i>
<i>d[u] := infinity</i>
<i>p[u] := u</i>
<i>color[u] :=</i> WHITE
<b>end for</b>
<i>color[s] := </i>GRAY
<i>d[s] := 0</i>
<i>color[s] := </i>GRAY
<i>d[s] := 0</i>
INSERT(<i>Q</i>, <i>s</i>)
<b>while</b> (<i>Q != &Oslash;</i>)
<i>u :=</i> EXTRACT-MIN(<i>Q</i>)
@ -136,10 +136,10 @@ DIJKSTRA(<i>G</i>, <i>s</i>, <i>w</i>)
<b>for</b> each vertex <i>v in Adj[u]</i>
<b>if</b> (<i>w(u,v) + d[u] < d[v]</i>)
<i>d[v] := w(u,v) + d[u]</i>
<i>p[v] := u</i>
<b>if</b> (<i>color[v] =</i> WHITE)
<i>p[v] := u</i>
<b>if</b> (<i>color[v] =</i> WHITE)
<i>color[v] :=</i> GRAY
INSERT(<i>Q</i>, <i>v</i>)
INSERT(<i>Q</i>, <i>v</i>)
<b>else if</b> (<i>color[v] =</i> GRAY)
DECREASE-KEY(<i>Q</i>, <i>v</i>)
<b>else</b>
@ -188,17 +188,17 @@ finish vertex <i>u</i>
<h3>Parameters</h3>
IN: <tt>const Graph&amp; g</tt>
IN: <tt>const Graph&amp; g</tt>
<blockquote>
The graph object on which the algorithm will be applied.
The type <tt>Graph</tt> must be a model of
The type <tt>Graph</tt> must be a model of
<a href="./VertexListGraph.html">Vertex List Graph</a>
and <a href="./IncidenceGraph.html">Incidence Graph</a>.<br>
<b>Python</b>: The parameter is named <tt>graph</tt>.
</blockquote>
IN: <tt>vertex_descriptor s</tt>
IN: <tt>vertex_descriptor s</tt>
<blockquote>
The source vertex. All distance will be calculated from this vertex,
and the shortest paths tree will be rooted at this vertex.<br>
@ -208,11 +208,11 @@ IN: <tt>vertex_descriptor s</tt>
<h3>Named Parameters</h3>
IN: <tt>weight_map(WeightMap w_map)</tt>
IN: <tt>weight_map(WeightMap w_map)</tt>
<blockquote>
The weight or ``length'' of each edge in the graph. The weights
must all be non-negative, and the algorithm will throw a
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
exception is one of the edges is negative.
The type <tt>WeightMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of
@ -225,13 +225,13 @@ IN: <tt>weight_map(WeightMap w_map)</tt>
<b>Python default</b>: <tt>graph.get_edge_double_map("weight")</tt>
</blockquote>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(g))</tt>. This is necessary for efficient updates of the
heap data structure&nbsp;[<A
HREF="bibliography.html#driscoll88">61</A>] when an edge is relaxed.
The type
The type
<tt>VertexIndexMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The value type of the map must be an
integer type. The vertex descriptor type of the graph needs to be
@ -246,10 +246,10 @@ IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<blockquote>
The predecessor map records the edges in the shortest path tree, the tree computed
by the traversal of the graph. Upon completion of the algorithm, the edges
by the traversal of the graph. Upon completion of the algorithm, the edges
<i>(p[u],u)</i> for all <i>u in V</i> are in the tree. The shortest path
from vertex <i>s</i> to each vertex <i>v</i> in the graph consists of the
vertices <i>v</i>, <i>p[v]</i>, <i>p[p[v]]</i>, and so on until <i>s</i> is
@ -266,7 +266,7 @@ OUT: <tt>predecessor_map(PredecessorMap p_map)</tt>
<b>Python</b>: Must be a <tt>vertex_vertex_map</tt> for the graph.<br>
</blockquote>
UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
<blockquote>
The shortest path weight from the source vertex <tt>s</tt> to each
vertex in the graph <tt>g</tt> is recorded in this property map. The
@ -274,7 +274,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
shortest path. The type <tt>DistanceMap</tt> must be a model of <a
href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
Property Map</a>. The vertex descriptor type of the graph needs to
be usable as the key type of the distance map.
be usable as the key type of the distance map.
The value type of the distance map is the element type of a <a
href="./Monoid.html">Monoid</a> formed with the <tt>combine</tt>
@ -293,7 +293,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap d_map)</tt>
<b>Python</b>: Must be a <tt>vertex_double_map</tt> for the graph.<br>
</blockquote>
IN: <tt>distance_compare(CompareFunction cmp)</tt>
IN: <tt>distance_compare(CompareFunction cmp)</tt>
<blockquote>
This function is use to compare distances to determine which vertex
is closer to the source vertex. The <tt>CompareFunction</tt> type
@ -309,7 +309,7 @@ IN: <tt>distance_compare(CompareFunction cmp)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_combine(CombineFunction cmb)</tt>
IN: <tt>distance_combine(CombineFunction cmb)</tt>
<blockquote>
This function is used to combine distances to compute the distance
of a path. The <tt>CombineFunction</tt> type must be a model of <a
@ -326,7 +326,7 @@ IN: <tt>distance_combine(CombineFunction cmb)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_inf(D inf)</tt>
IN: <tt>distance_inf(D inf)</tt>
<blockquote>
The <tt>inf</tt> object must be the greatest value of any <tt>D</tt> object.
That is, <tt>compare(d, inf) == true</tt> for any <tt>d != inf</tt>.
@ -338,7 +338,7 @@ IN: <tt>distance_inf(D inf)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
IN: <tt>distance_zero(D zero)</tt>
IN: <tt>distance_zero(D zero)</tt>
<blockquote>
The <tt>zero</tt> value must be the identity element for the
<a href="./Monoid.html">Monoid</a> formed by the distance values
@ -350,7 +350,7 @@ IN: <tt>distance_zero(D zero)</tt>
<b>Python</b>: Unsupported parameter.
</blockquote>
UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
<blockquote>
This is used during the execution of the algorithm to mark the
vertices. The vertices start out white and become gray when they are
@ -371,13 +371,13 @@ UTIL/OUT: <tt>color_map(ColorMap c_map)</tt>
<b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for
the graph.
</blockquote>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
<blockquote>
Use this to specify actions that you would like to happen
during certain event points within the algorithm.
The type <tt>DijkstraVisitor</tt> must be a model of the
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
The visitor object is passed by value <a
href="#2">[2]</a>.<br>
<b>Default:</b> <tt>dijkstra_visitor&lt;null_visitor&gt;</tt><br>
@ -404,19 +404,19 @@ The time complexity is <i>O(V log V + E)</i>.
<li><b><tt>vis.examine_vertex(u, g)</tt></b>
is invoked on a vertex as it is removed from the priority queue
and added to set <i>S</i>. At this point we know that <i>(p[u],u)</i>
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
of the examined vertices is monotonically increasing
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<li><b><tt>vis.examine_edge(e, g)</tt></b>
is invoked on each out-edge of a vertex immediately after it has
been added to set <i>S</i>.
been added to set <i>S</i>.
<li><b><tt>vis.edge_relaxed(e, g)</tt></b>
is invoked on edge <i>(u,v)</i> if <i>d[u] + w(u,v) < d[v]</i>.
The edge <i>(u,v)</i> that participated in the last
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
<li><b><tt>vis.discover_vertex(v, g)</tt></b>
is invoked on vertex <i>v</i> when the edge
is invoked on vertex <i>v</i> when the edge
<i>(u,v)</i> is examined and <i>v</i> is WHITE. Since
a vertex is colored GRAY when it is discovered,
each reachable vertex is discovered exactly once. This
@ -445,7 +445,7 @@ S</i> vertices in the priority queue at once, but instead only those
vertices in <i>V - S</i> that are discovered and therefore have a
distance less than infinity.
<p><a name="2">[2]</a>
<p><a name="2">[2]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
@ -461,4 +461,4 @@ distance less than infinity.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

94
doc/dijkstra_shortest_paths_no_color_map.html
View File

@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Michael Hansen 2009
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Dijkstra's Shortest Paths (No Color Map)</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -27,29 +27,29 @@ void dijkstra_shortest_paths_no_color_map
(const Graph&amp; graph,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start_vertex,
const bgl_named_params<Param,Tag,Rest>& params);
<i>// non-named parameter version</i>
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
typename PredecessorMap, typename DistanceMap,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">DistanceCompare</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">DistanceWeightCombine</a>,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">DistanceCompare</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">DistanceWeightCombine</a>,
typename DistanceInfinity, typename DistanceZero&gt;
void dijkstra_shortest_paths_no_color_map
(const Graph&amp; graph,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start_vertex,
PredecessorMap predecessor_map, DistanceMap distance_map, WeightMap weight_map,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start_vertex,
PredecessorMap predecessor_map, DistanceMap distance_map, WeightMap weight_map,
VertexIndexMap index_map,
DistanceCompare distance_compare, DistanceWeightCombine distance_weight_combine,
DistanceInfinity distance_infinity, DistanceZero distance_zero);
<i>// version that does not initialize the property maps</i>
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
template &lt;typename Graph, typename <a href="DijkstraVisitor.html">DijkstraVisitor</a>,
typename PredecessorMap, typename DistanceMap,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">DistanceCompare</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">DistanceWeightCombine</a>,
typename WeightMap, typename VertexIndexMap, typename <a href="http://www.boost.org/sgi/stl/BinaryPredicate.html">DistanceCompare</a>, typename <a href="http://www.boost.org/sgi/stl/BinaryFunction.html">DistanceWeightCombine</a>,
typename DistanceInfinity, typename DistanceZero&gt;
void dijkstra_shortest_paths_no_color_map_no_init
(const Graph&amp; graph,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start_vertex,
PredecessorMap predecessor_map, DistanceMap distance_map, WeightMap weight_map,
typename graph_traits&lt;Graph&gt;::vertex_descriptor start_vertex,
PredecessorMap predecessor_map, DistanceMap distance_map, WeightMap weight_map,
VertexIndexMap index_map,
DistanceCompare distance_compare, DistanceWeightCombine distance_weight_combine,
DistanceInfinity distance_infinity, DistanceZero distance_zero);
@ -116,16 +116,16 @@ indicated by the labels on the right.
<td valign="top">
<pre>
DIJKSTRA(<i>G</i>, <i>s</i>, <i>w</i>)
<i>d[s] := 0</i>
<i>d[s] := 0</i>
INSERT(<i>Q</i>, <i>s</i>)
<b>while</b> (<i>Q != &Oslash;</i>)
<i>u :=</i> EXTRACT-MIN(<i>Q</i>)
<b>for</b> each vertex <i>v in Adj[u]</i>
<b>if</b> (<i>w(u,v) + d[u] < d[v]</i>)
<i>d[v] := w(u,v) + d[u]</i>
<i>p[v] := u</i>
<b>if</b> (<i>d[v]</i> was originally infinity)
INSERT(<i>Q</i>, <i>v</i>)
<i>p[v] := u</i>
<b>if</b> (<i>d[v]</i> was originally infinity)
INSERT(<i>Q</i>, <i>v</i>)
<b>else</b>
DECREASE-KEY(<i>Q</i>, <i>v</i>)
<b>else</b>
@ -164,15 +164,15 @@ finish vertex <i>u</i>
<h3>Parameters</h3>
IN: <tt>const Graph&amp; graph</tt>
IN: <tt>const Graph&amp; graph</tt>
<blockquote>
The graph object on which the algorithm will be applied.
The type <tt>Graph</tt> must be a model of
The type <tt>Graph</tt> must be a model of
<a href="./VertexListGraph.html">Vertex List Graph</a>
and <a href="./IncidenceGraph.html">Incidence Graph</a>.<br>
</blockquote>
IN: <tt>vertex_descriptor start_vertex</tt>
IN: <tt>vertex_descriptor start_vertex</tt>
<blockquote>
The source vertex. All distance will be calculated from this vertex,
and the shortest paths tree will be rooted at this vertex.<br>
@ -180,11 +180,11 @@ IN: <tt>vertex_descriptor start_vertex</tt>
<h3>Named Parameters</h3>
IN: <tt>weight_map(WeightMap weight_map)</tt>
IN: <tt>weight_map(WeightMap weight_map)</tt>
<blockquote>
The weight or ``length'' of each edge in the graph. The weights
must all be non-negative and non-infinite <a href="#3">[3]</a>. The algorithm will throw a
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
<a href="./exception.html#negative_edge"><tt>negative_edge</tt></a>
exception is one of the edges is negative.
The type <tt>WeightMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The edge descriptor type of
@ -194,13 +194,13 @@ IN: <tt>weight_map(WeightMap weight_map)</tt>
<b>Default:</b> <tt>get(edge_weight, graph)</tt><br>
</blockquote>
IN: <tt>index_map(VertexIndexMap index_map)</tt>
IN: <tt>index_map(VertexIndexMap index_map)</tt>
<blockquote>
This maps each vertex to an integer in the range <tt>[0,
num_vertices(graph))</tt>. This is necessary for efficient updates of the
heap data structure&nbsp;[<A
HREF="bibliography.html#driscoll88">61</A>] when an edge is relaxed.
The type
The type
<tt>VertexIndexMap</tt> must be a model of
<a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map</a>. The value type of the map must be an
integer type. The vertex descriptor type of the graph needs to be
@ -213,7 +213,7 @@ IN: <tt>index_map(VertexIndexMap index_map)</tt>
<br>
</blockquote>
OUT: <tt>predecessor_map(PredecessorMap predecessor_map)</tt>
OUT: <tt>predecessor_map(PredecessorMap predecessor_map)</tt>
<blockquote>
The predecessor map records the edges in the minimum spanning
tree. Upon completion of the algorithm, the edges <i>(p[u],u)</i>
@ -229,7 +229,7 @@ OUT: <tt>predecessor_map(PredecessorMap predecessor_map)</tt>
<b>Python</b>: Must be a <tt>vertex_vertex_map</tt> for the graph.<br>
</blockquote>
UTIL/OUT: <tt>distance_map(DistanceMap distance_map)</tt>
UTIL/OUT: <tt>distance_map(DistanceMap distance_map)</tt>
<blockquote>
The shortest path weight from the source vertex <tt>start_vertex</tt> to each
vertex in the graph <tt>graph</tt> is recorded in this property map. The
@ -237,7 +237,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap distance_map)</tt>
shortest path. The type <tt>DistanceMap</tt> must be a model of <a
href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
Property Map</a>. The vertex descriptor type of the graph needs to
be usable as the key type of the distance map.
be usable as the key type of the distance map.
The value type of the distance map is the element type of a <a
href="./Monoid.html">Monoid</a> formed with the <tt>distance_weight_combine</tt>
@ -254,7 +254,7 @@ UTIL/OUT: <tt>distance_map(DistanceMap distance_map)</tt>
map.<br>
</blockquote>
IN: <tt>distance_compare(CompareFunction distance_compare)</tt>
IN: <tt>distance_compare(CompareFunction distance_compare)</tt>
<blockquote>
This function is use to compare distances to determine which vertex
is closer to the source vertex. The <tt>DistanceCompareFunction</tt> type
@ -268,7 +268,7 @@ IN: <tt>distance_compare(CompareFunction distance_compare)</tt>
property_traits&lt;DistanceMap&gt;::value_type</tt><br>
</blockquote>
IN: <tt>distance_combine(CombineFunction distance_weight_combine)</tt>
IN: <tt>distance_combine(CombineFunction distance_weight_combine)</tt>
<blockquote>
This function is used to combine distances to compute the distance
of a path. The <tt>DistanceWeightCombineFunction</tt> type must be a model of <a
@ -283,7 +283,7 @@ IN: <tt>distance_combine(CombineFunction distance_weight_combine)</tt>
<tt>D=typename property_traits&lt;DistanceMap&gt;::value_type</tt><br>
</blockquote>
IN: <tt>distance_inf(D distance_infinity)</tt>
IN: <tt>distance_inf(D distance_infinity)</tt>
<blockquote>
The <tt>distance_infinity</tt> object must be the greatest value of any <tt>D</tt> object.
That is, <tt>distance_compare(d, distance_infinity) == true</tt> for any <tt>d != distance_infinity</tt>.
@ -293,7 +293,7 @@ IN: <tt>distance_inf(D distance_infinity)</tt>
<b>Default:</b> <tt>std::numeric_limits&lt;D&gt;::max()</tt><br>
</blockquote>
IN: <tt>distance_zero(D distance_zero)</tt>
IN: <tt>distance_zero(D distance_zero)</tt>
<blockquote>
The <tt>distance_zero</tt> value must be the identity element for the
<a href="./Monoid.html">Monoid</a> formed by the distance values
@ -302,13 +302,13 @@ IN: <tt>distance_zero(D distance_zero)</tt>
<b>Default:</b> <tt>D()</tt>with
<tt>D=typename property_traits&lt;DistanceMap&gt;::value_type</tt><br>
</blockquote>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
OUT: <tt>visitor(DijkstraVisitor v)</tt>
<blockquote>
Use this to specify actions that you would like to happen
during certain event points within the algorithm.
The type <tt>DijkstraVisitor</tt> must be a model of the
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
<a href="./DijkstraVisitor.html">Dijkstra Visitor</a> concept.
The visitor object is passed by value <a
href="#2">[2]</a>.<br>
<b>Default:</b> <tt>dijkstra_visitor&lt;null_visitor&gt;</tt><br>
@ -330,19 +330,19 @@ The time complexity is <i>O(V log V + E)</i>.
<li><b><tt>vis.examine_vertex(u, g)</tt></b>
is invoked on a vertex as it is removed from the priority queue
and added to set <i>S</i>. At this point we know that <i>(p[u],u)</i>
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
is a shortest-paths tree edge so
<i>d[u] = delta(s,u) = d[p[u]] + w(p[u],u)</i>. Also, the distances
of the examined vertices is monotonically increasing
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<i>d[u<sub>1</sub>] <= d[u<sub>2</sub>] <= d[u<sub>n</sub>]</i>.
<li><b><tt>vis.examine_edge(e, g)</tt></b>
is invoked on each out-edge of a vertex immediately after it has
been added to set <i>S</i>.
been added to set <i>S</i>.
<li><b><tt>vis.edge_relaxed(e, g)</tt></b>
is invoked on edge <i>(u,v)</i> if <i>d[u] + w(u,v) < d[v]</i>.
The edge <i>(u,v)</i> that participated in the last
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
relaxation for vertex <i>v</i> is an edge in the shortest paths tree.
<li><b><tt>vis.discover_vertex(v, g)</tt></b>
is invoked on vertex <i>v</i> when the edge
is invoked on vertex <i>v</i> when the edge
<i>(u,v)</i> is examined and <i>v</i> has not yet been discovered (i.e. its distance was infinity before relaxation was attempted on the edge). This
is also when the vertex is inserted into the priority queue.
<li><b><tt>vis.edge_not_relaxed(e, g)</tt></b>
@ -370,17 +370,17 @@ S</i> vertices in the priority queue at once, but instead only those
vertices in <i>V - S</i> that are discovered and therefore have a
distance less than infinity.
<p><a name="2">[2]</a>
<p><a name="2">[2]</a>
Since the visitor parameter is passed by value, if your visitor
contains state then any changes to the state during the algorithm
will be made to a copy of the visitor object, not the visitor object
passed in. Therefore you may want the visitor to hold this state by
pointer or reference.
<p><a name="3">[3]</a>
<p><a name="3">[3]</a>
The algorithm will not work correctly if any of the edge weights are equal to infinity since the infinite distance value is used to determine if a vertex has been discovered.
<p><a name="4">[4]</a>
<p><a name="4">[4]</a>
Calls to the visitor events occur in the same order as <tt>dijkstra_shortest_paths</tt> (i.e. <i>discover_vertex(u)</i> will always be called after <i>examine_vertex(u)</i> for an undiscovered vertex <i>u</i>). However, the vertices of the graph given to <i>dijkstra_shortest_paths_no_color_map</i> will <b>not</b> necessarily be visited in the same order as <i>dijkstra_shortest_paths</i>.
<br>
@ -391,4 +391,4 @@ distance less than infinity.
Trustees of Indiana University</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

14
doc/dijkstra_visitor.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: dijkstra_visitor</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -37,7 +37,7 @@ by Dijkstra's algorithm.
<pre>
boost::dijkstra_shortest_paths
(G, vertex(a, G),
(G, vertex(a, G),
distance_map(make_iterator_property_map(distance.begin(), vertex_id, distance[0])).
predecessor_map(make_iterator_property_map(parent.begin(), vertex_id, parent[0])).
visitor(make_dijkstra_visitor(copy_graph(G_copy, on_examine_edge()))));
@ -122,4 +122,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/directed_graph.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) David Doria 2012
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Directed Graph</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -93,4 +93,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

4
doc/disjoint_sets.html
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@ -73,7 +73,7 @@ disjoint_sets&lt;Rank, Parent, FindCompress&gt;
<pre>
...
disjoint_sets&lt;Rank, Parent, FindCompress&gt; dsets(rank, p);
for (ui = vertices(G).first; ui != vertices(G).second; ++ui)
dsets.make_set(*ui);
...
@ -282,7 +282,7 @@ Element operator()(Parent p, Element x)
"../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional"
height="31" width="88"></a></p>
<p>Revised
<p>Revised
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->01
December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38508" --></p>

2
doc/disjoint_sets_biblio.html
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@ -37,7 +37,7 @@
"../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional"
height="31" width="88"></a></p>
<p>Revised
<p>Revised
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->01
December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38508" --></p>

14
doc/distance_recorder.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: distance_recorder</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -124,7 +124,7 @@ template &lt;class Edge, class Graph&gt;<br>
void operator()(Edge e, const Graph& g);
</tt></td>
<td>
Given edge <i>e = (u,v)</i>, this records the distance of <i>v</i> as
Given edge <i>e = (u,v)</i>, this records the distance of <i>v</i> as
one plus the distance of <i>u</i>.
</td>
</tr>
@ -173,7 +173,7 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>
<!-- LocalWords: DistanceMap EventTag EventVisitor map bfs dfs const Siek
-->
<!-- LocalWords: EventVisitorList WritablePropertyMap Univ Quan

22
doc/edge_list.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Edge List Class</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -52,7 +52,7 @@ Applying the Bellman-Ford shortest paths algorithm to an
E(x,y), E(x,v),
E(y,v), E(y,z),
E(z,u), E(z,x) };
int weight[] = { -4, 8, 5,
-2,
9, -3,
@ -61,16 +61,16 @@ Applying the Bellman-Ford shortest paths algorithm to an
typedef boost::edge_list&lt;E*&gt; Graph;
Graph g(edges, edges + sizeof(edges) / sizeof(E));
std::vector&lt;int&gt; distance(N, std::numeric_limits&lt;short&gt;::max());
std::vector&lt;int&gt; parent(N,-1);
distance[z] = 0;
parent[z] = z;
bool r = boost::bellman_ford_shortest_paths(g, int(N), weight,
distance.begin(),
parent.begin());
if (r)
if (r)
for (int i = 0; i &lt; N; ++i)
std::cout &lt;&lt; name[i] &lt;&lt; ": " &lt;&lt; distance[i]
&lt;&lt; " " &lt;&lt; name[parent[i]] &lt;&lt; std::endl;
@ -145,7 +145,7 @@ boost::graph_traits&lt;edge_list&gt;::edge_descriptor
</tt>
<br><br>
The type for the edge descriptors associated with the
<TT>edge_list</TT>.
<TT>edge_list</TT>.
<hr>
@ -218,4 +218,4 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

12
doc/edge_predecessor_recorder.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: edge_predecessor_recorder</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -188,7 +188,7 @@ HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>
<!-- LocalWords: PredEdgeMap EventTag EventVisitor map bfs dfs const
-->
<!-- LocalWords: EventVisitorList WritablePropertyMap Siek Univ Quan

28
doc/edmonds_karp_max_flow.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Edmonds-Karp Maximum Flow</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -23,20 +23,20 @@
<i>// named parameter version</i>
template &lt;class <a href="./Graph.html">Graph</a>, class P, class T, class R&gt;
typename detail::edge_capacity_value&lt;Graph, P, T, R&gt;::value_type
edmonds_karp_max_flow(Graph& g,
edmonds_karp_max_flow(Graph& g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor src,
typename graph_traits&lt;Graph&gt;::vertex_descriptor sink,
const bgl_named_params&lt;P, T, R&gt;&amp; params = <i>all defaults</i>)
<i>// non-named parameter version</i>
template &lt;class <a href="./Graph.html">Graph</a>,
template &lt;class <a href="./Graph.html">Graph</a>,
class CapacityEdgeMap, class ResidualCapacityEdgeMap,
class ReverseEdgeMap, class ColorMap, class PredEdgeMap&gt;
typename property_traits&lt;CapacityEdgeMap&gt;::value_type
edmonds_karp_max_flow(Graph&amp; g,
edmonds_karp_max_flow(Graph&amp; g,
typename graph_traits&lt;Graph&gt;::vertex_descriptor src,
typename graph_traits&lt;Graph&gt;::vertex_descriptor sink,
CapacityEdgeMap cap, ResidualCapacityEdgeMap res, ReverseEdgeMap rev,
CapacityEdgeMap cap, ResidualCapacityEdgeMap res, ReverseEdgeMap rev,
ColorMap color, PredEdgeMap pred)
</PRE>
@ -48,7 +48,7 @@ Flow Algorithms</a> for a description of maximum flow. The calculated
maximum flow will be the return value of the function. The function
also calculates the flow values <i>f(u,v)</i> for all <i>(u,v)</i> in
<i>E</i>, which are returned in the form of the residual capacity
<i>r(u,v) = c(u,v) - f(u,v)</i>.
<i>r(u,v) = c(u,v) - f(u,v)</i>.
<p>
There are several special requirements on the input graph and property
@ -112,12 +112,12 @@ IN: <tt>vertex_descriptor src</tt>
<blockquote>
The source vertex for the flow network graph.
</blockquote>
IN: <tt>vertex_descriptor sink</tt>
<blockquote>
The sink vertex for the flow network graph.
</blockquote>
<h3>Named Parameters</h3>
@ -129,7 +129,7 @@ IN: <tt>capacity_map(CapacityEdgeMap cap)</tt>
key type of the map must be the graph's edge descriptor type.<br>
<b>Default:</b> <tt>get(edge_capacity, g)</tt>
</blockquote>
OUT: <tt>residual_capacity_map(ResidualCapacityEdgeMap res)</tt>
<blockquote>
This maps edges to their residual capacity. The type must be a model
@ -228,7 +228,7 @@ from a file in the DIMACS format and computes the maximum flow.
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>
<!-- LocalWords: HTML Siek Edmonds BGCOLOR ffffff ee VLINK ALINK ff IMG SRC
-->
<!-- LocalWords: gif ALT BR sec edmonds karp TT DIV CELLPADDING TR TD PRE lt

138
doc/eg1-iso.cpp
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@ -30,77 +30,95 @@
using namespace boost;
enum { a, b, c, d, e, f, g, h };
enum { _1, _2, _3, _4, _5, _6, _7, _8 };
void test_isomorphism()
enum
{
typedef adjacency_list<vecS, vecS, bidirectionalS> GraphA;
typedef adjacency_list<vecS, vecS, bidirectionalS> GraphB;
a,
b,
c,
d,
e,
f,
g,
h
};
enum
{
_1,
_2,
_3,
_4,
_5,
_6,
_7,
_8
};
char a_names[] = "abcdefgh";
char b_names[] = "12345678";
void test_isomorphism()
{
typedef adjacency_list< vecS, vecS, bidirectionalS > GraphA;
typedef adjacency_list< vecS, vecS, bidirectionalS > GraphB;
GraphA Ga(8);
add_edge(a, d, Ga);
add_edge(a, h, Ga);
add_edge(b, c, Ga);
add_edge(b, e, Ga);
add_edge(c, f, Ga);
add_edge(d, a, Ga);
add_edge(d, h, Ga);
add_edge(e, b, Ga);
add_edge(f, b, Ga);
add_edge(f, e, Ga);
add_edge(g, d, Ga);
add_edge(g, f, Ga);
add_edge(h, c, Ga);
add_edge(h, g, Ga);
char a_names[] = "abcdefgh";
char b_names[] = "12345678";
GraphB Gb(8);
add_edge(_1, _6, Gb);
add_edge(_2, _1, Gb);
add_edge(_2, _5, Gb);
add_edge(_3, _2, Gb);
add_edge(_3, _4, Gb);
add_edge(_4, _2, Gb);
add_edge(_4, _3, Gb);
add_edge(_5, _4, Gb);
add_edge(_5, _6, Gb);
add_edge(_6, _7, Gb);
add_edge(_6, _8, Gb);
add_edge(_7, _8, Gb);
add_edge(_8, _1, Gb);
add_edge(_8, _7, Gb);
GraphA Ga(8);
add_edge(a, d, Ga);
add_edge(a, h, Ga);
add_edge(b, c, Ga);
add_edge(b, e, Ga);
add_edge(c, f, Ga);
add_edge(d, a, Ga);
add_edge(d, h, Ga);
add_edge(e, b, Ga);
add_edge(f, b, Ga);
add_edge(f, e, Ga);
add_edge(g, d, Ga);
add_edge(g, f, Ga);
add_edge(h, c, Ga);
add_edge(h, g, Ga);
std::vector<std::size_t> in_degree_A(num_vertices(Ga));
boost::detail::compute_in_degree(Ga, &in_degree_A[0]);
GraphB Gb(8);
add_edge(_1, _6, Gb);
add_edge(_2, _1, Gb);
add_edge(_2, _5, Gb);
add_edge(_3, _2, Gb);
add_edge(_3, _4, Gb);
add_edge(_4, _2, Gb);
add_edge(_4, _3, Gb);
add_edge(_5, _4, Gb);
add_edge(_5, _6, Gb);
add_edge(_6, _7, Gb);
add_edge(_6, _8, Gb);
add_edge(_7, _8, Gb);
add_edge(_8, _1, Gb);
add_edge(_8, _7, Gb);
std::vector<std::size_t> in_degree_B(num_vertices(Gb));
boost::detail::compute_in_degree(Gb, &in_degree_B[0]);
std::vector< std::size_t > in_degree_A(num_vertices(Ga));
boost::detail::compute_in_degree(Ga, &in_degree_A[0]);
degree_vertex_invariant<std::size_t*, GraphA>
invariantA(&in_degree_A[0], Ga);
degree_vertex_invariant<std::size_t*, GraphB>
invariantB(&in_degree_B[0], Gb);
std::vector< std::size_t > in_degree_B(num_vertices(Gb));
boost::detail::compute_in_degree(Gb, &in_degree_B[0]);
std::vector<graph_traits<GraphB>::vertex_descriptor> f(num_vertices(Ga));
degree_vertex_invariant< std::size_t*, GraphA > invariantA(
&in_degree_A[0], Ga);
degree_vertex_invariant< std::size_t*, GraphB > invariantB(
&in_degree_B[0], Gb);
bool ret = isomorphism(Ga, Gb, &f[0], invariantA, invariantB,
(invariantB.max)(),
get(vertex_index, Ga), get(vertex_index, Gb));
assert(ret == true);
std::vector< graph_traits< GraphB >::vertex_descriptor > f(
num_vertices(Ga));
for (std::size_t i = 0; i < num_vertices(Ga); ++i)
std::cout << "f(" << a_names[i] << ")=" << b_names[f[i]] << std::endl;
BOOST_TEST(verify_isomorphism(Ga, Gb, &f[0]));
bool ret = isomorphism(Ga, Gb, &f[0], invariantA, invariantB,
(invariantB.max)(), get(vertex_index, Ga), get(vertex_index, Gb));
assert(ret == true);
for (std::size_t i = 0; i < num_vertices(Ga); ++i)
std::cout << "f(" << a_names[i] << ")=" << b_names[f[i]] << std::endl;
BOOST_TEST(verify_isomorphism(Ga, Gb, &f[0]));
}
int test_main(int, char* [])
int test_main(int, char*[])
{
test_isomorphism();
return boost::report_errors();
test_isomorphism();
return boost::report_errors();
}

16
doc/erdos_renyi_generator.html
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@ -1,11 +1,11 @@
<HTML>
<!--
Copyright (c) 2004, 2005 The Trustees of Indiana University
Use, modification and distribution is subject to the Boost Software
License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
Authors: Douglas Gregor
Jeremiah Willcock
Andrew Lumsdaine
@ -24,10 +24,10 @@ function address(host, user) {
</script>
</head>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<tt>erdos_renyi_iterator</tt>
@ -57,7 +57,7 @@ public:
erdos_renyi_iterator operator++(int);
bool operator==(const erdos_renyi_iterator&amp; other) const;
bool operator!=(const erdos_renyi_iterator&amp; other) const;
};
};
</PRE>
<p> This class template implements a generator for Erd&ouml;s-Renyi
@ -149,4 +149,4 @@ Indiana University (<script language="Javascript">address("osl.iu.edu", "lums")<
</TD></TR></TABLE>
</BODY>
</HTML>
</HTML>

10
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek 2002
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: Exceptions</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>

18
doc/faq.html
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@ -1,17 +1,17 @@
<HTML>
<!--
Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<Head>
<Title>Boost Graph Library: FAQ</Title>
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
ALINK="#ff0000">
<IMG SRC="../../../boost.png"
ALT="C++ Boost" width="277" height="86">
<BR Clear>
@ -76,8 +76,8 @@ convenient. Granted, this is not a huge difference, but since there
weren't other strong reasons, it was enough for us to choose free
functions.
</p>
<p>
<p>
Our religious reason for choosing free functions is to send the message
that BGL is a generic library, and not a traditional object-oriented
library. OO was hip in the 80s and 90s, but its time we moved beyond!
@ -124,13 +124,13 @@ library. OO was hip in the 80s and 90s, but its time we moved beyond!
not being found, such as:
<pre>
../../../boost/concept_check.hpp:209: no match for
`boost::detail::error_property_not_found &amp; ==
`boost::detail::error_property_not_found &amp; ==
boost::detail::error_property_not_found &amp;'
</pre>
or a message such as:
<pre>
../../..\boost/graph/depth_first_search.hpp(78) : error C2664: 'white'
: cannot convert parameter 1 from
: cannot convert parameter 1 from
'struct boost::detail::error_property_not_found'
to 'enum boost::default_color_type'
</pre>

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