384 lines
13 KiB
C++
384 lines
13 KiB
C++
//=======================================================================
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// Copyright (c) 2005 Aaron Windsor
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//
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// Distributed under the Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//
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//=======================================================================
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#include <boost/config.hpp>
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#ifdef BOOST_MSVC
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// Without disabling this we get hard errors about initialialized pointers:
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#pragma warning(disable:4703)
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#endif
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#include <boost/graph/max_cardinality_matching.hpp>
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#include <iostream> // for std::cout
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#include <boost/property_map/vector_property_map.hpp>
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#include <boost/graph/adjacency_list.hpp>
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#include <boost/graph/adjacency_matrix.hpp>
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#include <boost/graph/random.hpp>
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#include <ctime>
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#include <boost/random.hpp>
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#include <boost/test/minimal.hpp>
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using namespace boost;
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typedef adjacency_list<vecS,
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vecS,
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undirectedS,
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property<vertex_index_t, int> > undirected_graph;
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typedef adjacency_list<listS,
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listS,
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undirectedS,
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property<vertex_index_t, int> > undirected_list_graph;
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typedef adjacency_matrix<undirectedS,
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property<vertex_index_t,int> > undirected_adjacency_matrix_graph;
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template <typename Graph>
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struct vertex_index_installer
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{
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static void install(Graph&) {}
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};
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template <>
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struct vertex_index_installer<undirected_list_graph>
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{
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static void install(undirected_list_graph& g)
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{
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typedef graph_traits<undirected_list_graph>::vertex_iterator vertex_iterator_t;
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typedef graph_traits<undirected_list_graph>::vertices_size_type v_size_t;
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vertex_iterator_t vi, vi_end;
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v_size_t i = 0;
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for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi, ++i)
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put(vertex_index, g, *vi, i);
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}
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};
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template <typename Graph>
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void complete_graph(Graph& g, int n)
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{
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//creates the complete graph on n vertices
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typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
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g = Graph(n);
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vertex_iterator_t vi, vi_end, wi;
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boost::tie(vi,vi_end) = vertices(g);
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for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
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{
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wi = vi;
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++wi;
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for(; wi != vi_end; ++wi)
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add_edge(*vi,*wi,g);
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}
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}
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template <typename Graph>
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void gabows_graph(Graph& g, int n)
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{
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//creates a graph with 2n vertices, consisting of the complete graph
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//on n vertices plus n vertices of degree one, each adjacent to one
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//vertex in the complete graph. without any initial matching, this
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//graph forces edmonds' algorithm into worst-case behavior.
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typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
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g = Graph(2* n);
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vertex_iterator_t vi, vi_end, ui, ui_end, halfway;
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boost::tie(ui,ui_end) = vertices(g);
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halfway = ui;
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for(int i = 0; i < n; ++i)
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++halfway;
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while(ui != halfway)
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{
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vi = ui;
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++vi;
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while (vi != halfway)
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{
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add_edge(*ui,*vi,g);
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++vi;
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}
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++ui;
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}
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boost::tie(ui,ui_end) = vertices(g);
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while(halfway != ui_end)
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{
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add_edge(*ui, *halfway, g);
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++ui;
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++halfway;
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}
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}
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template <typename Graph>
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void matching_test(std::size_t num_v, const std::string& graph_name)
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{
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typedef typename property_map<Graph,vertex_index_t>::type vertex_index_map_t;
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typedef vector_property_map< typename graph_traits<Graph>::vertex_descriptor, vertex_index_map_t > mate_t;
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typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
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typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor_t;
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const std::size_t double_num_v = num_v * 2;
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bool all_tests_passed = true;
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//form the complete graph on 2*n vertices; the maximum cardinality matching, greedy matching,
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//and extra greedy matching should all be the same - a matching of size n.
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Graph g(double_num_v);
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complete_graph(g,double_num_v);
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vertex_index_installer<Graph>::install(g);
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mate_t edmonds_mate(double_num_v);
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mate_t greedy_mate(double_num_v);
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mate_t extra_greedy_mate(double_num_v);
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//find a maximum cardinality matching using edmonds' blossom-shrinking algorithm, starting
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//with an empty matching.
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bool edmonds_result =
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matching < Graph, mate_t, vertex_index_map_t,
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edmonds_augmenting_path_finder, empty_matching, maximum_cardinality_matching_verifier>
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(g,edmonds_mate, get(vertex_index,g));
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BOOST_CHECK (edmonds_result);
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if (!edmonds_result)
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{
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std::cout << "Verifier reporting a problem finding a perfect matching on" << std::endl
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<< "the complete graph using " << graph_name << std::endl;
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all_tests_passed = false;
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}
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//find a greedy matching
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bool greedy_result =
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matching<Graph, mate_t, vertex_index_map_t,
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no_augmenting_path_finder, greedy_matching, maximum_cardinality_matching_verifier>
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(g,greedy_mate, get(vertex_index,g));
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BOOST_CHECK (greedy_result);
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if (!greedy_result)
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{
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std::cout << "Verifier reporting a problem finding a greedy matching on" << std::endl
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<< "the complete graph using " << graph_name << std::endl;
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all_tests_passed = false;
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}
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//find an extra greedy matching
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bool extra_greedy_result =
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matching<Graph, mate_t, vertex_index_map_t,
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no_augmenting_path_finder, extra_greedy_matching, maximum_cardinality_matching_verifier>
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(g,extra_greedy_mate,get(vertex_index,g));
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BOOST_CHECK (extra_greedy_result);
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if (!extra_greedy_result)
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{
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std::cout << "Verifier reporting a problem finding an extra greedy matching on" << std::endl
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<< "the complete graph using " << graph_name << std::endl;
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all_tests_passed = false;
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}
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//as a sanity check, make sure that each of the matchings returned is a valid matching and has
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//1000 edges.
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bool edmonds_sanity_check =
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is_a_matching(g,edmonds_mate) && matching_size(g,edmonds_mate) == num_v;
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BOOST_CHECK (edmonds_sanity_check);
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if (edmonds_result && !edmonds_sanity_check)
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{
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std::cout << "Verifier okayed edmonds' algorithm on the complete graph, but" << std::endl
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<< "the matching returned either wasn't a valid matching or wasn't" << std::endl
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<< "actually a maximum cardinality matching." << std::endl;
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all_tests_passed = false;
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}
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bool greedy_sanity_check =
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is_a_matching(g,greedy_mate) && matching_size(g,greedy_mate) == num_v;
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BOOST_CHECK (greedy_sanity_check);
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if (greedy_result && !greedy_sanity_check)
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{
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std::cout << "Verifier okayed greedy algorithm on the complete graph, but" << std::endl
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<< "the matching returned either wasn't a valid matching or wasn't" << std::endl
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<< "actually a maximum cardinality matching." << std::endl;
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all_tests_passed = false;
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}
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bool extra_greedy_sanity_check =
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is_a_matching(g,extra_greedy_mate) && matching_size(g,extra_greedy_mate) == num_v;
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BOOST_CHECK (extra_greedy_sanity_check);
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if (extra_greedy_result && !extra_greedy_sanity_check)
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{
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std::cout << "Verifier okayed extra greedy algorithm on the complete graph, but" << std::endl
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<< "the matching returned either wasn't a valid matching or wasn't" << std::endl
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<< "actually a maximum cardinality matching." << std::endl;
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all_tests_passed = false;
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}
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//Now remove an edge from the edmonds_mate matching.
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vertex_iterator_t vi,vi_end;
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for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
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if (edmonds_mate[*vi] != graph_traits<Graph>::null_vertex())
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break;
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edmonds_mate[edmonds_mate[*vi]] = graph_traits<Graph>::null_vertex();
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edmonds_mate[*vi] = graph_traits<Graph>::null_vertex();
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//...and run the matching verifier - it should tell us that the matching isn't
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//a maximum matching.
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bool modified_edmonds_verification_result =
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maximum_cardinality_matching_verifier<Graph,mate_t,vertex_index_map_t>::verify_matching(g,edmonds_mate,get(vertex_index,g));
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BOOST_CHECK (!modified_edmonds_verification_result);
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if (modified_edmonds_verification_result)
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{
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std::cout << "Verifier was fooled into thinking that a non-maximum matching was maximum" << std::endl;
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all_tests_passed = false;
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}
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Graph h(double_num_v);
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gabows_graph(h,num_v);
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vertex_index_installer<Graph>::install(h);
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//gabow's graph always has a perfect matching. it's also a good example of why
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//one should initialize with the extra_greedy_matching in most cases.
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mate_t gabow_mate(double_num_v);
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bool gabows_graph_result = checked_edmonds_maximum_cardinality_matching(h,gabow_mate);
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BOOST_CHECK (gabows_graph_result);
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if (!gabows_graph_result)
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{
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std::cout << "Problem on Gabow's Graph with " << graph_name << ":" << std::endl
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<< " Verifier reporting a maximum cardinality matching not found." << std::endl;
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all_tests_passed = false;
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}
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BOOST_CHECK (matching_size(h,gabow_mate) == num_v);
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if (gabows_graph_result && matching_size(h,gabow_mate) != num_v)
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{
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std::cout << "Problem on Gabow's Graph with " << graph_name << ":" << std::endl
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<< " Verifier reported a maximum cardinality matching found," << std::endl
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<< " but matching size is " << matching_size(h,gabow_mate)
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<< " when it should be " << num_v << std::endl;
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all_tests_passed = false;
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}
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Graph j(double_num_v);
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vertex_index_installer<Graph>::install(j);
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typedef boost::mt19937 base_generator_type;
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base_generator_type generator(static_cast<unsigned int>(std::time(0)));
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boost::uniform_int<> distribution(0, double_num_v-1);
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boost::variate_generator<base_generator_type&, boost::uniform_int<> > rand_num(generator, distribution);
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std::size_t num_edges = 0;
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bool success;
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while (num_edges < 4*double_num_v)
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{
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vertex_descriptor_t u = random_vertex(j,rand_num);
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vertex_descriptor_t v = random_vertex(j,rand_num);
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if (u != v)
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{
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boost::tie(tuples::ignore, success) = add_edge(u, v, j);
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if (success)
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num_edges++;
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}
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}
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mate_t random_mate(double_num_v);
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bool random_graph_result = checked_edmonds_maximum_cardinality_matching(j,random_mate);
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BOOST_CHECK(random_graph_result);
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if (!random_graph_result)
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{
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std::cout << "Matching in random graph not maximum for " << graph_name << std::endl;
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all_tests_passed = false;
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}
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//Now remove an edge from the random_mate matching.
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for(boost::tie(vi,vi_end) = vertices(j); vi != vi_end; ++vi)
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if (random_mate[*vi] != graph_traits<Graph>::null_vertex())
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break;
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random_mate[random_mate[*vi]] = graph_traits<Graph>::null_vertex();
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random_mate[*vi] = graph_traits<Graph>::null_vertex();
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//...and run the matching verifier - it should tell us that the matching isn't
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//a maximum matching.
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bool modified_random_verification_result =
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maximum_cardinality_matching_verifier<Graph,mate_t,vertex_index_map_t>::verify_matching(j,random_mate,get(vertex_index,j));
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BOOST_CHECK(!modified_random_verification_result);
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if (modified_random_verification_result)
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{
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std::cout << "Verifier was fooled into thinking that a non-maximum matching was maximum" << std::endl;
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all_tests_passed = false;
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}
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BOOST_CHECK(all_tests_passed);
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if (all_tests_passed)
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{
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std::cout << graph_name << " passed all tests for n = " << num_v << '.' << std::endl;
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}
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}
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int test_main(int, char*[])
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{
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matching_test<undirected_graph>(10, "adjacency_list (using vectors)");
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matching_test<undirected_list_graph>(10, "adjacency_list (using lists)");
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matching_test<undirected_adjacency_matrix_graph>(10, "adjacency_matrix");
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matching_test<undirected_graph>(20, "adjacency_list (using vectors)");
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matching_test<undirected_list_graph>(20, "adjacency_list (using lists)");
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matching_test<undirected_adjacency_matrix_graph>(20, "adjacency_matrix");
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matching_test<undirected_graph>(21, "adjacency_list (using vectors)");
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matching_test<undirected_list_graph>(21, "adjacency_list (using lists)");
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matching_test<undirected_adjacency_matrix_graph>(21, "adjacency_matrix");
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#if 0
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matching_test<undirected_graph>(50, "adjacency_list (using vectors)");
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matching_test<undirected_list_graph>(50, "adjacency_list (using lists)");
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matching_test<undirected_adjacency_matrix_graph>(50, "adjacency_matrix");
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matching_test<undirected_graph>(51, "adjacency_list (using vectors)");
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matching_test<undirected_list_graph>(51, "adjacency_list (using lists)");
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matching_test<undirected_adjacency_matrix_graph>(51, "adjacency_matrix");
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#endif
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return 0;
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}
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