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