| // Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman | |
| // | |
| // 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) | |
| #ifndef BOOST_GRAPH_ISOMORPHISM_HPP | |
| #define BOOST_GRAPH_ISOMORPHISM_HPP | |
| #include <utility> | |
| #include <vector> | |
| #include <iterator> | |
| #include <algorithm> | |
| #include <boost/config.hpp> | |
| #include <boost/graph/depth_first_search.hpp> | |
| #include <boost/utility.hpp> | |
| #include <boost/detail/algorithm.hpp> | |
| #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap | |
| #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP | |
| #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file | |
| #include <boost/graph/iteration_macros.hpp> | |
| #endif | |
| namespace boost { | |
| namespace detail { | |
| template <typename Graph1, typename Graph2, typename IsoMapping, | |
| typename Invariant1, typename Invariant2, | |
| typename IndexMap1, typename IndexMap2> | |
| class isomorphism_algo | |
| { | |
| typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t; | |
| typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t; | |
| typedef typename graph_traits<Graph1>::edge_descriptor edge1_t; | |
| typedef typename graph_traits<Graph1>::vertices_size_type size_type; | |
| typedef typename Invariant1::result_type invar1_value; | |
| typedef typename Invariant2::result_type invar2_value; | |
| const Graph1& G1; | |
| const Graph2& G2; | |
| IsoMapping f; | |
| Invariant1 invariant1; | |
| Invariant2 invariant2; | |
| std::size_t max_invariant; | |
| IndexMap1 index_map1; | |
| IndexMap2 index_map2; | |
| std::vector<vertex1_t> dfs_vertices; | |
| typedef typename std::vector<vertex1_t>::iterator vertex_iter; | |
| std::vector<int> dfs_num_vec; | |
| typedef safe_iterator_property_map<typename std::vector<int>::iterator, | |
| IndexMap1 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , int, int& | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| > DFSNumMap; | |
| DFSNumMap dfs_num; | |
| std::vector<edge1_t> ordered_edges; | |
| typedef typename std::vector<edge1_t>::iterator edge_iter; | |
| std::vector<char> in_S_vec; | |
| typedef safe_iterator_property_map<typename std::vector<char>::iterator, | |
| IndexMap2 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , char, char& | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| > InSMap; | |
| InSMap in_S; | |
| int num_edges_on_k; | |
| friend struct compare_multiplicity; | |
| struct compare_multiplicity | |
| { | |
| compare_multiplicity(Invariant1 invariant1, size_type* multiplicity) | |
| : invariant1(invariant1), multiplicity(multiplicity) { } | |
| bool operator()(const vertex1_t& x, const vertex1_t& y) const { | |
| return multiplicity[invariant1(x)] < multiplicity[invariant1(y)]; | |
| } | |
| Invariant1 invariant1; | |
| size_type* multiplicity; | |
| }; | |
| struct record_dfs_order : default_dfs_visitor | |
| { | |
| record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) | |
| : vertices(v), edges(e) { } | |
| void discover_vertex(vertex1_t v, const Graph1&) const { | |
| vertices.push_back(v); | |
| } | |
| void examine_edge(edge1_t e, const Graph1&) const { | |
| edges.push_back(e); | |
| } | |
| std::vector<vertex1_t>& vertices; | |
| std::vector<edge1_t>& edges; | |
| }; | |
| struct edge_cmp { | |
| edge_cmp(const Graph1& G1, DFSNumMap dfs_num) | |
| : G1(G1), dfs_num(dfs_num) { } | |
| bool operator()(const edge1_t& e1, const edge1_t& e2) const { | |
| using namespace std; | |
| int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)]; | |
| int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)]; | |
| int m1 = (max)(u1, v1); | |
| int m2 = (max)(u2, v2); | |
| // lexicographical comparison | |
| return std::make_pair(m1, std::make_pair(u1, v1)) | |
| < std::make_pair(m2, std::make_pair(u2, v2)); | |
| } | |
| const Graph1& G1; | |
| DFSNumMap dfs_num; | |
| }; | |
| public: | |
| isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f, | |
| Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant, | |
| IndexMap1 index_map1, IndexMap2 index_map2) | |
| : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2), | |
| max_invariant(max_invariant), | |
| index_map1(index_map1), index_map2(index_map2) | |
| { | |
| in_S_vec.resize(num_vertices(G1)); | |
| in_S = make_safe_iterator_property_map | |
| (in_S_vec.begin(), in_S_vec.size(), index_map2 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , in_S_vec.front() | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| ); | |
| } | |
| bool test_isomorphism() | |
| { | |
| { | |
| std::vector<invar1_value> invar1_array; | |
| BGL_FORALL_VERTICES_T(v, G1, Graph1) | |
| invar1_array.push_back(invariant1(v)); | |
| sort(invar1_array); | |
| std::vector<invar2_value> invar2_array; | |
| BGL_FORALL_VERTICES_T(v, G2, Graph2) | |
| invar2_array.push_back(invariant2(v)); | |
| sort(invar2_array); | |
| if (! equal(invar1_array, invar2_array)) | |
| return false; | |
| } | |
| std::vector<vertex1_t> V_mult; | |
| BGL_FORALL_VERTICES_T(v, G1, Graph1) | |
| V_mult.push_back(v); | |
| { | |
| std::vector<size_type> multiplicity(max_invariant, 0); | |
| BGL_FORALL_VERTICES_T(v, G1, Graph1) | |
| ++multiplicity[invariant1(v)]; | |
| sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0])); | |
| } | |
| std::vector<default_color_type> color_vec(num_vertices(G1)); | |
| safe_iterator_property_map<std::vector<default_color_type>::iterator, | |
| IndexMap1 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , default_color_type, default_color_type& | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| > | |
| color_map(color_vec.begin(), color_vec.size(), index_map1); | |
| record_dfs_order dfs_visitor(dfs_vertices, ordered_edges); | |
| typedef color_traits<default_color_type> Color; | |
| for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) { | |
| if (color_map[*u] == Color::white()) { | |
| dfs_visitor.start_vertex(*u, G1); | |
| depth_first_visit(G1, *u, dfs_visitor, color_map); | |
| } | |
| } | |
| // Create the dfs_num array and dfs_num_map | |
| dfs_num_vec.resize(num_vertices(G1)); | |
| dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(), | |
| dfs_num_vec.size(), | |
| index_map1 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , dfs_num_vec.front() | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| ); | |
| size_type n = 0; | |
| for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v) | |
| dfs_num[*v] = n++; | |
| sort(ordered_edges, edge_cmp(G1, dfs_num)); | |
| int dfs_num_k = -1; | |
| return this->match(ordered_edges.begin(), dfs_num_k); | |
| } | |
| private: | |
| bool match(edge_iter iter, int dfs_num_k) | |
| { | |
| if (iter != ordered_edges.end()) { | |
| vertex1_t i = source(*iter, G1), j = target(*iter, G2); | |
| if (dfs_num[i] > dfs_num_k) { | |
| vertex1_t kp1 = dfs_vertices[dfs_num_k + 1]; | |
| BGL_FORALL_VERTICES_T(u, G2, Graph2) { | |
| if (invariant1(kp1) == invariant2(u) && in_S[u] == false) { | |
| f[kp1] = u; | |
| in_S[u] = true; | |
| num_edges_on_k = 0; | |
| if (match(iter, dfs_num_k + 1)) | |
| #if 0 | |
| // dwa 2003/7/11 -- this *HAS* to be a bug! | |
| ; | |
| #endif | |
| return true; | |
| in_S[u] = false; | |
| } | |
| } | |
| } | |
| else if (dfs_num[j] > dfs_num_k) { | |
| vertex1_t k = dfs_vertices[dfs_num_k]; | |
| num_edges_on_k -= | |
| count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S)); | |
| for (int jj = 0; jj < dfs_num_k; ++jj) { | |
| vertex1_t j = dfs_vertices[jj]; | |
| num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]); | |
| } | |
| if (num_edges_on_k != 0) | |
| return false; | |
| BGL_FORALL_ADJ_T(f[i], v, G2, Graph2) | |
| if (invariant2(v) == invariant1(j) && in_S[v] == false) { | |
| f[j] = v; | |
| in_S[v] = true; | |
| num_edges_on_k = 1; | |
| BOOST_USING_STD_MAX(); | |
| int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j])); | |
| if (match(boost::next(iter), next_k)) | |
| return true; | |
| in_S[v] = false; | |
| } | |
| } | |
| else { | |
| if (container_contains(adjacent_vertices(f[i], G2), f[j])) { | |
| ++num_edges_on_k; | |
| if (match(boost::next(iter), dfs_num_k)) | |
| return true; | |
| } | |
| } | |
| } else | |
| return true; | |
| return false; | |
| } | |
| }; | |
| template <typename Graph, typename InDegreeMap> | |
| void compute_in_degree(const Graph& g, InDegreeMap in_degree_map) | |
| { | |
| BGL_FORALL_VERTICES_T(v, g, Graph) | |
| put(in_degree_map, v, 0); | |
| BGL_FORALL_VERTICES_T(u, g, Graph) | |
| BGL_FORALL_ADJ_T(u, v, g, Graph) | |
| put(in_degree_map, v, get(in_degree_map, v) + 1); | |
| } | |
| } // namespace detail | |
| template <typename InDegreeMap, typename Graph> | |
| class degree_vertex_invariant | |
| { | |
| typedef typename graph_traits<Graph>::vertex_descriptor vertex_t; | |
| typedef typename graph_traits<Graph>::degree_size_type size_type; | |
| public: | |
| typedef vertex_t argument_type; | |
| typedef size_type result_type; | |
| degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g) | |
| : m_in_degree_map(in_degree_map), | |
| m_max_vertex_in_degree(0), | |
| m_max_vertex_out_degree(0), | |
| m_g(g) { | |
| BGL_FORALL_VERTICES_T(v, g, Graph) { | |
| m_max_vertex_in_degree = | |
| (std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v)); | |
| m_max_vertex_out_degree = | |
| (std::max)(m_max_vertex_out_degree, out_degree(v, g)); | |
| } | |
| } | |
| size_type operator()(vertex_t v) const { | |
| return (m_max_vertex_in_degree + 1) * out_degree(v, m_g) | |
| + get(m_in_degree_map, v); | |
| } | |
| // The largest possible vertex invariant number | |
| size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { | |
| return (m_max_vertex_in_degree + 2) * m_max_vertex_out_degree + 1; | |
| } | |
| private: | |
| InDegreeMap m_in_degree_map; | |
| size_type m_max_vertex_in_degree; | |
| size_type m_max_vertex_out_degree; | |
| const Graph& m_g; | |
| }; | |
| template <typename Graph1, typename Graph2, typename IsoMapping, | |
| typename Invariant1, typename Invariant2, | |
| typename IndexMap1, typename IndexMap2> | |
| bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, | |
| Invariant1 invariant1, Invariant2 invariant2, | |
| std::size_t max_invariant, | |
| IndexMap1 index_map1, IndexMap2 index_map2) | |
| { | |
| // Graph requirements | |
| function_requires< VertexListGraphConcept<Graph1> >(); | |
| function_requires< EdgeListGraphConcept<Graph1> >(); | |
| function_requires< VertexListGraphConcept<Graph2> >(); | |
| function_requires< BidirectionalGraphConcept<Graph2> >(); | |
| typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t; | |
| typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t; | |
| typedef typename graph_traits<Graph1>::vertices_size_type size_type; | |
| // Vertex invariant requirement | |
| function_requires< AdaptableUnaryFunctionConcept<Invariant1, | |
| size_type, vertex1_t> >(); | |
| function_requires< AdaptableUnaryFunctionConcept<Invariant2, | |
| size_type, vertex2_t> >(); | |
| // Property map requirements | |
| function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >(); | |
| typedef typename property_traits<IsoMapping>::value_type IsoMappingValue; | |
| BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value)); | |
| function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >(); | |
| typedef typename property_traits<IndexMap1>::value_type IndexMap1Value; | |
| BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value)); | |
| function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >(); | |
| typedef typename property_traits<IndexMap2>::value_type IndexMap2Value; | |
| BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value)); | |
| if (num_vertices(G1) != num_vertices(G2)) | |
| return false; | |
| if (num_vertices(G1) == 0 && num_vertices(G2) == 0) | |
| return true; | |
| detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1, | |
| Invariant2, IndexMap1, IndexMap2> | |
| algo(G1, G2, f, invariant1, invariant2, max_invariant, | |
| index_map1, index_map2); | |
| return algo.test_isomorphism(); | |
| } | |
| namespace detail { | |
| template <typename Graph1, typename Graph2, | |
| typename IsoMapping, | |
| typename IndexMap1, typename IndexMap2, | |
| typename P, typename T, typename R> | |
| bool isomorphism_impl(const Graph1& G1, const Graph2& G2, | |
| IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2, | |
| const bgl_named_params<P,T,R>& params) | |
| { | |
| std::vector<std::size_t> in_degree1_vec(num_vertices(G1)); | |
| typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, | |
| IndexMap1 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , std::size_t, std::size_t& | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| > InDeg1; | |
| InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1); | |
| compute_in_degree(G1, in_degree1); | |
| std::vector<std::size_t> in_degree2_vec(num_vertices(G2)); | |
| typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, | |
| IndexMap2 | |
| #ifdef BOOST_NO_STD_ITERATOR_TRAITS | |
| , std::size_t, std::size_t& | |
| #endif /* BOOST_NO_STD_ITERATOR_TRAITS */ | |
| > InDeg2; | |
| InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2); | |
| compute_in_degree(G2, in_degree2); | |
| degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1); | |
| degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2); | |
| return isomorphism(G1, G2, f, | |
| choose_param(get_param(params, vertex_invariant1_t()), invariant1), | |
| choose_param(get_param(params, vertex_invariant2_t()), invariant2), | |
| choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()), | |
| index_map1, index_map2 | |
| ); | |
| } | |
| } // namespace detail | |
| // Named parameter interface | |
| template <typename Graph1, typename Graph2, class P, class T, class R> | |
| bool isomorphism(const Graph1& g1, | |
| const Graph2& g2, | |
| const bgl_named_params<P,T,R>& params) | |
| { | |
| typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t; | |
| typename std::vector<vertex2_t>::size_type n = num_vertices(g1); | |
| std::vector<vertex2_t> f(n); | |
| return detail::isomorphism_impl | |
| (g1, g2, | |
| choose_param(get_param(params, vertex_isomorphism_t()), | |
| make_safe_iterator_property_map(f.begin(), f.size(), | |
| choose_const_pmap(get_param(params, vertex_index1), | |
| g1, vertex_index), vertex2_t())), | |
| choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index), | |
| choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index), | |
| params | |
| ); | |
| } | |
| // All defaults interface | |
| template <typename Graph1, typename Graph2> | |
| bool isomorphism(const Graph1& g1, const Graph2& g2) | |
| { | |
| return isomorphism(g1, g2, | |
| bgl_named_params<int, buffer_param_t>(0));// bogus named param | |
| } | |
| // Verify that the given mapping iso_map from the vertices of g1 to the | |
| // vertices of g2 describes an isomorphism. | |
| // Note: this could be made much faster by specializing based on the graph | |
| // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm, | |
| // O(n^4) won't hurt us. | |
| template<typename Graph1, typename Graph2, typename IsoMap> | |
| inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map) | |
| { | |
| #if 0 | |
| // problematic for filtered_graph! | |
| if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2)) | |
| return false; | |
| #endif | |
| BGL_FORALL_EDGES_T(e1, g1, Graph1) { | |
| bool found_edge = false; | |
| BGL_FORALL_EDGES_T(e2, g2, Graph2) { | |
| if (source(e2, g2) == get(iso_map, source(e1, g1)) && | |
| target(e2, g2) == get(iso_map, target(e1, g1))) { | |
| found_edge = true; | |
| } | |
| } | |
| if (!found_edge) | |
| return false; | |
| } | |
| return true; | |
| } | |
| } // namespace boost | |
| #ifdef BOOST_ISO_INCLUDED_ITER_MACROS | |
| #undef BOOST_ISO_INCLUDED_ITER_MACROS | |
| #include <boost/graph/iteration_macros_undef.hpp> | |
| #endif | |
| #endif // BOOST_GRAPH_ISOMORPHISM_HPP |