diff --git a/doc/maximum_weighted_matching.html b/doc/maximum_weighted_matching.html index 32e60799..79d934e6 100644 --- a/doc/maximum_weighted_matching.html +++ b/doc/maximum_weighted_matching.html @@ -21,7 +21,7 @@ void maximum_weighted_matching(const Graph& g, MateMap mate); template <typename Graph, typename MateMap, typename VertexIndexMap> void maximum_weighted_matching(const Graph& g, MateMap mate, VertexIndexMap vm); -template <typename Graph, typename MateMap, typename VertexIndexMap, typename EdgeWeightMap, bool Verify = true> +template <typename Graph, typename MateMap, typename VertexIndexMap, typename EdgeWeightMap> void maximum_weighted_matching(const Graph& g, MateMap mate, VertexIndexMap vm, EdgeWeightMap weights); template <typename Graph, typename MateMap> @@ -121,13 +121,6 @@ If edge weights are integers, the algorithm uses only integer computations. This is achieved by internally multiplying edge weights by 2, which ensures that all dual variables are also integers.

-

-After computing the maximum matching, a verification step may be performed to check that the matching is optimal. -The verification step is simpler and faster (O(V2)) than the search for the matching. -It always succeeds unless there is a bug in the matching algorithm. -Since verification checks for exact optimality, it can only be used if edge weights are integers. -

-

In addition, a brute-force implementation brute_force_maximum_weighted_matching is provided. This algorithm simply searches all possible matchings and selects one with the maximum weight sum. diff --git a/include/boost/graph/maximum_weighted_matching.hpp b/include/boost/graph/maximum_weighted_matching.hpp index 0135cf8e..a3e10d4e 100644 --- a/include/boost/graph/maximum_weighted_matching.hpp +++ b/include/boost/graph/maximum_weighted_matching.hpp @@ -24,7 +24,6 @@ #include #include #include -#include #include // for std::tie #include // for std::pair, std::swap #include @@ -1405,235 +1404,6 @@ struct maximum_weighted_matching_context for (vertex_t x : make_iterator_range(vertices(g))) put(mate, x, vertex_mate[x]); } - - /** Check that the array "vertex_mate" is consistent. */ - bool verify_vertex_mate() - { - vertices_size_t num_matched_vertex = 0; - for (vertex_t x : make_iterator_range(vertices(g))) - { - vertex_t y = vertex_mate[x]; - if (y != null_vertex) - { - ++num_matched_vertex; - if (vertex_mate[y] != x) - return false; - } - } - - edges_size_t num_matched_edge = 0; - for (const edge_t& e : make_iterator_range(edges(g))) - { - if (vertex_mate[source(e, g)] == target(e, g)) - ++num_matched_edge; - } - - return num_matched_vertex == 2 * num_matched_edge; - } - - /** - * Verify that vertex dual variables are non-negative, - * and all unmatched vertices have zero dual. - */ - bool verify_vertex_duals() - { - for (vertex_t x : make_iterator_range(vertices(g))) - { - if (vertex_dual[x] < 0) - return false; - if ((vertex_mate[x] == null_vertex) && (vertex_dual[x] != 0)) - return false; - } - return true; - } - - /** Verify that blossom dual variables are non-negative. */ - bool verify_blossom_duals() - { - for (const nontrivial_blossom_t& blossom : nontrivial_blossom) - { - if (blossom.dual_var < 0) - return false; - } - return true; - } - - /** Verify slack of edges between trivial blossoms. */ - bool verify_trivial_blossom_edges() - { - for (const edge_t& e : make_iterator_range(edges(g))) - { - vertex_t x = source(e, g); - vertex_t y = target(e, g); - if ((! trivial_blossom[x].parent) && (! trivial_blossom[y].parent)) - { - weight_t w = weight_factor * get(edge_weights, e); - weight_t dual_sum = vertex_dual[x] + vertex_dual[y]; - // Edge slack must be non-negative. - if (w > dual_sum) - return false; - // Matched edges must have slack zero. - if ((vertex_mate[x] == y) && (w != dual_sum)) - return false; - } - } - return true; - } - - /** Verify one top-level blossom and its edges. */ - bool verify_blossom(const nontrivial_blossom_t* blossom) - { - // This function recursively descends down the blossom structure. - // It checks the number of matched edges in every sub-blossom. - // It also checks the slack of edges contained in this blossom - // and of edges incident on this blossom. - - // For each vertex, deepest level on current recursion path - // that contains the vertex. - vertex_map< vertices_size_t > vertex_depth(num_vertices(g), vm); - - // At each recursion depth, sum of duals of containing blossoms. - std::vector< weight_t > path_sum_dual = {0}; - - // At each recursion depth, number of internally matched vertices. - std::vector< vertices_size_t > path_num_matched = {0}; - - // Use an explicit stack to avoid deep call chains. - using sub_blossom_iterator = typename std::list< - typename nontrivial_blossom_t::sub_blossom_t >::const_iterator; - std::stack< std::pair< - const nontrivial_blossom_t*, sub_blossom_iterator > > stack; - - stack.emplace(blossom, blossom->subblossoms.cbegin()); - while (! stack.empty()) - { - vertices_size_t depth = stack.size(); - blossom = stack.top().first; - auto subblossom_it = stack.top().second; - - if (subblossom_it == blossom->subblossoms.cbegin()) - { - // Entering a new (sub)-blossom. - if (blossom->subblossoms.size() < 3) { - return false; - } - - // Update the depth of vertices in this sub-blossom. - for_vertices_in_blossom(blossom, - [&vertex_depth,depth](vertex_t x) { - vertex_depth[x] = depth; - }); - - // Calculate the sum of blossom duals at the new depth. - path_sum_dual.push_back( - path_sum_dual.back() + blossom->dual_var); - - // Initialize the number of matched edges at the new depth. - path_num_matched.push_back(0); - } - - if (subblossom_it != blossom->subblossoms.cend()) - { - // Update the sub-blossom pointer at the current depth. - ++(stack.top().second); - - // Examine a sub-blossom. - blossom_t* b = subblossom_it->blossom; - BOOST_ASSERT(b->parent == blossom); - nontrivial_blossom_t* ntb = b->nontrivial(); - if (ntb) - { - // Prepare to descend into the sub-blossom. - stack.emplace(ntb, ntb->subblossoms.cbegin()); - } - else - { - // Handle single vertex. - vertex_t x = b->base_vertex; - for (const edge_t& e : make_iterator_range(out_edges(x, g))) - { - BOOST_ASSERT(source(e, g) == x); - vertex_t y = target(e, g); - // Find the smallest blossom that contains this edge. - vertices_size_t edge_depth = vertex_depth[y]; - // Verify edge slack. - weight_t w = weight_factor * get(edge_weights, e); - weight_t dual_sum = vertex_dual[x] + vertex_dual[y] - + path_sum_dual[edge_depth]; - // Edge slack must be non-negative. - if (w > dual_sum) - return false; - // Matched edges must have slack zero. - if ((vertex_mate[x] == y) && (w != dual_sum)) - return false; - // Update number of internally matched vertices. - if ((vertex_mate[x] == y) && (edge_depth > 0)) - path_num_matched[edge_depth] += 1; - } - } - } - else - { - // Leaving the current (sub)-blossom. - // Count the number of vertices inside this blossom. - vertices_size_t blossom_num_vertex = 0; - for_vertices_in_blossom(blossom, - [&blossom_num_vertex](vertex_t) { - ++blossom_num_vertex; - }); - - // Check that the (sub)-blossom is "full". - // A blossom is full if all except one of its vertices - // are matched to another vertex within the blossom. - vertices_size_t blossom_num_matched = path_num_matched[depth]; - if (blossom_num_vertex != blossom_num_matched + 1) - return false; - - // Update the number of matched edges in the parent blossom. - path_num_matched[depth - 1] += path_num_matched[depth]; - - // Restore the depth of vertices. - for_vertices_in_blossom(blossom, - [&vertex_depth,depth](vertex_t x) { - vertex_depth[x] = depth - 1; - }); - - // Remove the blossom from the stack. - path_sum_dual.pop_back(); - path_num_matched.pop_back(); - stack.pop(); - } - } - - return true; - } - - /** Verify blossoms and their edges. */ - bool verify_blossoms() - { - // Recursively verify each non-trivial top-level blossom. - // This takes total time O(V^2). - for (const nontrivial_blossom_t& blossom : nontrivial_blossom) - { - if (! blossom.parent) - { - if (! verify_blossom(&blossom)) - return false; - } - } - return true; - } - - /** Verify that the optimum solution has been found. */ - bool verify() - { - return (verify_vertex_mate() - && verify_vertex_duals() - && verify_blossom_duals() - && verify_trivial_blossom_edges() - && verify_blossoms()); - return true; - } }; } // namespace detail @@ -1645,11 +1415,6 @@ struct maximum_weighted_matching_context * This function takes time O(V^3). * This function uses memory size O(V + E). * - * @tparam Verify True to verify the matching. - * This is only supported for integer edge weights. - * Verification will always succeed unless there is a bug - * in the matching algorithm. - * * @param g Input graph. * The graph type must be a model of VertexListGraph * and EdgeListGraph and IncidenceGraph. @@ -1670,7 +1435,7 @@ struct maximum_weighted_matching_context * @throw boost::bad_graph If the input graph is not valid. */ template < typename Graph, typename MateMap, typename VertexIndexMap, - typename EdgeWeightMap, bool Verify = true > + typename EdgeWeightMap > void maximum_weighted_matching( const Graph& g, MateMap mate, VertexIndexMap vm, EdgeWeightMap weights) { @@ -1695,14 +1460,6 @@ void maximum_weighted_matching( Graph, VertexIndexMap, EdgeWeightMap > matching(g, vm, weights); matching.run(); - - typedef typename property_traits< EdgeWeightMap >::value_type weight_t; - if (Verify && std::numeric_limits< weight_t >::is_integer) - { - if (! matching.verify()) - throw std::logic_error("Incorrect solution."); - } - matching.extract_matching(mate); }