http://www.ousob.com --- Legacy Redefined OuSob - File: /wwwroot/clipx/usr/include/boost/graph/isomorphism.hpp

// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman // // Permission to copy, use, sell and distribute this software is granted // provided this copyright notice appears in all copies. // Permission to modify the code and to distribute modified code is granted // provided this copyright notice appears in all copies, and a notice // that the code was modified is included with the copyright notice. // // This software is provided "as is" without express or implied warranty, // and with no claim as to its suitability for any purpose. #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& G1) 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(next(iter), next_k)) return true; in_S[v] = false; } } else { if (contains(adjacent_vertices(f[i], G2), f[j])) { ++num_edges_on_k; if (match(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_g(g) { } size_type operator()(vertex_t v) const { return (num_vertices(m_g) + 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 num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g); } private: InDegreeMap m_in_degree_map; 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 for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first; e1 != edges(g1).second; ++e1) { bool found_edge = false; for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first; e2 != edges(g2).second && !found_edge; ++e2) { 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