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some examples for maximum weighted matching

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jiyi 2018-06-24 23:25:26 +09:00
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//=======================================================================
// Copyright (c) 2018 Yi Ji
//
// 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)
//
//=======================================================================
#include <iostream>
#include <vector>
#include <string>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/maximum_weighted_matching.hpp>
using namespace boost;
typedef property<edge_weight_t, float, property<edge_index_t, int> > EdgeProperty;
typedef adjacency_list<vecS, vecS, undirectedS, no_property, EdgeProperty> my_graph;
int main(int argc, const char * argv[])
{
graph_traits<my_graph>::vertex_iterator vi, vi_end;
const int n_vertices = 18;
my_graph g(n_vertices);
// vertices can be refered by integers because my_graph use vector to store them
add_edge(1, 2, EdgeProperty(5), g);
add_edge(0, 4, EdgeProperty(1), g);
add_edge(1, 5, EdgeProperty(4), g);
add_edge(2, 6, EdgeProperty(1), g);
add_edge(3, 7, EdgeProperty(4), g);
add_edge(4, 5, EdgeProperty(7), g);
add_edge(6, 7, EdgeProperty(5), g);
add_edge(4, 8, EdgeProperty(2), g);
add_edge(5, 9, EdgeProperty(5), g);
add_edge(6, 10, EdgeProperty(6), g);
add_edge(7, 11, EdgeProperty(5), g);
add_edge(10, 11, EdgeProperty(4), g);
add_edge(8, 13, EdgeProperty(4), g);
add_edge(9, 14, EdgeProperty(4), g);
add_edge(10, 15, EdgeProperty(7), g);
add_edge(11, 16, EdgeProperty(6), g);
add_edge(14, 15, EdgeProperty(6), g);
add_edge(12, 13, EdgeProperty(2), g);
add_edge(16, 17, EdgeProperty(5), g);
// print the ascii graph into terminal (better to use fixed-width font)
// this graph has a maximum cardinality matching of size 8
// but maximum weighted matching is of size 7
std::vector<std::string> ascii_graph_weighted;
ascii_graph_weighted.push_back(" 5 ");
ascii_graph_weighted.push_back(" A B---C D ");
ascii_graph_weighted.push_back(" 1\\ 7 /4 1\\ 5 /4 ");
ascii_graph_weighted.push_back(" E---F G---H ");
ascii_graph_weighted.push_back(" 2| |5 6| |5 ");
ascii_graph_weighted.push_back(" I J K---L ");
ascii_graph_weighted.push_back(" 4/ 3\\ 7/ 4 \\6 ");
ascii_graph_weighted.push_back(" M---N O---P Q---R ");
ascii_graph_weighted.push_back(" 2 6 5 ");
// our maximum weighted matching and result
std::cout << "In the following graph:" << std::endl << std::endl;
for(std::vector<std::string>::iterator itr = ascii_graph_weighted.begin(); itr != ascii_graph_weighted.end(); ++itr)
std::cout << *itr << std::endl;
std::cout << std::endl;
std::vector<graph_traits<my_graph>::vertex_descriptor> mate1(n_vertices), mate2(n_vertices);
maximum_weighted_matching(g, &mate1[0]);
std::cout << "Found a weighted matching:" << std::endl;
std::cout << "Matching size is " << matching_size(g, &mate1[0]) << ", total weight is " << matching_weight_sum(g, &mate1[0]) << std::endl;
std::cout << std::endl;
std::cout << "The matching is:" << std::endl;
for (boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
if (mate1[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate1[*vi])
std::cout << "{" << *vi << ", " << mate1[*vi] << "}" << std::endl;
std::cout << std::endl;
// now we check the correctness by compare the weight sum to a brute-force matching result
// note that two matchings may be different because of multiple optimal solutions
brute_force_maximum_weighted_matching(g, &mate2[0]);
std::cout << "Found a weighted matching by brute-force searching:" << std::endl;
std::cout << "Matching size is " << matching_size(g, &mate2[0]) << ", total weight is " << matching_weight_sum(g, &mate2[0]) << std::endl;
std::cout << std::endl;
std::cout << "The brute-force matching is:" << std::endl;
for (boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
if (mate2[*vi] != graph_traits<my_graph>::null_vertex() && *vi < mate2[*vi])
std::cout << "{" << *vi << ", " << mate2[*vi] << "}" << std::endl;
std::cout << std::endl;
assert(matching_weight_sum(g, &mate1[0]) == matching_weight_sum(g, &mate2[0]));
return 0;
}