sl@0: // Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
sl@0: //
sl@0: // Distributed under the Boost Software License, Version 1.0. (See
sl@0: // accompanying file LICENSE_1_0.txt or copy at
sl@0: // http://www.boost.org/LICENSE_1_0.txt)
sl@0: #ifndef BOOST_GRAPH_ISOMORPHISM_HPP
sl@0: #define BOOST_GRAPH_ISOMORPHISM_HPP
sl@0: 
sl@0: #include <utility>
sl@0: #include <vector>
sl@0: #include <iterator>
sl@0: #include <algorithm>
sl@0: #include <boost/config.hpp>
sl@0: #include <boost/graph/depth_first_search.hpp>
sl@0: #include <boost/utility.hpp>
sl@0: #include <boost/detail/algorithm.hpp>
sl@0: #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
sl@0: 
sl@0: #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
sl@0: #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
sl@0: #include <boost/graph/iteration_macros.hpp>
sl@0: #endif
sl@0: 
sl@0: namespace boost {
sl@0: 
sl@0:   namespace detail {
sl@0: 
sl@0:     template <typename Graph1, typename Graph2, typename IsoMapping,
sl@0:       typename Invariant1, typename Invariant2,
sl@0:       typename IndexMap1, typename IndexMap2>
sl@0:     class isomorphism_algo
sl@0:     {
sl@0:       typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
sl@0:       typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
sl@0:       typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
sl@0:       typedef typename graph_traits<Graph1>::vertices_size_type size_type;
sl@0:       typedef typename Invariant1::result_type invar1_value;
sl@0:       typedef typename Invariant2::result_type invar2_value;
sl@0:     
sl@0:       const Graph1& G1;
sl@0:       const Graph2& G2;
sl@0:       IsoMapping f;
sl@0:       Invariant1 invariant1;
sl@0:       Invariant2 invariant2;
sl@0:       std::size_t max_invariant;
sl@0:       IndexMap1 index_map1;
sl@0:       IndexMap2 index_map2;
sl@0:     
sl@0:       std::vector<vertex1_t> dfs_vertices;
sl@0:       typedef typename std::vector<vertex1_t>::iterator vertex_iter;
sl@0:       std::vector<int> dfs_num_vec;
sl@0:       typedef safe_iterator_property_map<typename std::vector<int>::iterator,
sl@0:                                          IndexMap1
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                          , int, int&
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                          > DFSNumMap;
sl@0:       DFSNumMap dfs_num;
sl@0:       std::vector<edge1_t> ordered_edges;
sl@0:       typedef typename std::vector<edge1_t>::iterator edge_iter;
sl@0:     
sl@0:       std::vector<char> in_S_vec;
sl@0:       typedef safe_iterator_property_map<typename std::vector<char>::iterator,
sl@0:                                          IndexMap2
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                          , char, char&
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                          > InSMap;
sl@0:       InSMap in_S;
sl@0:     
sl@0:       int num_edges_on_k;
sl@0:     
sl@0:       friend struct compare_multiplicity;
sl@0:       struct compare_multiplicity
sl@0:       {
sl@0:         compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
sl@0:           : invariant1(invariant1), multiplicity(multiplicity) { }
sl@0:         bool operator()(const vertex1_t& x, const vertex1_t& y) const {
sl@0:           return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
sl@0:         }
sl@0:         Invariant1 invariant1;
sl@0:         size_type* multiplicity;
sl@0:       };
sl@0:     
sl@0:       struct record_dfs_order : default_dfs_visitor
sl@0:       {
sl@0:         record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 
sl@0:           : vertices(v), edges(e) { }
sl@0:     
sl@0:         void discover_vertex(vertex1_t v, const Graph1&) const {
sl@0:           vertices.push_back(v);
sl@0:         }
sl@0:         void examine_edge(edge1_t e, const Graph1& G1) const {
sl@0:           edges.push_back(e);
sl@0:         }
sl@0:         std::vector<vertex1_t>& vertices;
sl@0:         std::vector<edge1_t>& edges;
sl@0:       };
sl@0:     
sl@0:       struct edge_cmp {
sl@0:         edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
sl@0:           : G1(G1), dfs_num(dfs_num) { }
sl@0:         bool operator()(const edge1_t& e1, const edge1_t& e2) const {
sl@0:           using namespace std;
sl@0:           int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
sl@0:           int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
sl@0:           int m1 = (max)(u1, v1);
sl@0:           int m2 = (max)(u2, v2);
sl@0:           // lexicographical comparison 
sl@0:           return std::make_pair(m1, std::make_pair(u1, v1))
sl@0:             < std::make_pair(m2, std::make_pair(u2, v2));
sl@0:         }
sl@0:         const Graph1& G1;
sl@0:         DFSNumMap dfs_num;
sl@0:       };
sl@0:     
sl@0:     public:
sl@0:       isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
sl@0:                        Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
sl@0:                        IndexMap1 index_map1, IndexMap2 index_map2)
sl@0:         : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
sl@0:           max_invariant(max_invariant),
sl@0:           index_map1(index_map1), index_map2(index_map2)
sl@0:       {
sl@0:         in_S_vec.resize(num_vertices(G1));
sl@0:         in_S = make_safe_iterator_property_map
sl@0:           (in_S_vec.begin(), in_S_vec.size(), index_map2
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:            , in_S_vec.front()
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:            );
sl@0:       }
sl@0:     
sl@0:       bool test_isomorphism()
sl@0:       {
sl@0:         {
sl@0:           std::vector<invar1_value> invar1_array;
sl@0:           BGL_FORALL_VERTICES_T(v, G1, Graph1)
sl@0:             invar1_array.push_back(invariant1(v));
sl@0:           sort(invar1_array);
sl@0:         
sl@0:           std::vector<invar2_value> invar2_array;
sl@0:           BGL_FORALL_VERTICES_T(v, G2, Graph2)
sl@0:             invar2_array.push_back(invariant2(v));
sl@0:           sort(invar2_array);
sl@0:           if (! equal(invar1_array, invar2_array))
sl@0:             return false;
sl@0:         }
sl@0:         
sl@0:         std::vector<vertex1_t> V_mult;
sl@0:         BGL_FORALL_VERTICES_T(v, G1, Graph1)
sl@0:           V_mult.push_back(v);
sl@0:         {
sl@0:           std::vector<size_type> multiplicity(max_invariant, 0);
sl@0:           BGL_FORALL_VERTICES_T(v, G1, Graph1)
sl@0:             ++multiplicity[invariant1(v)];
sl@0:           sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
sl@0:         }
sl@0:         
sl@0:         std::vector<default_color_type> color_vec(num_vertices(G1));
sl@0:         safe_iterator_property_map<std::vector<default_color_type>::iterator,
sl@0:                                    IndexMap1
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                    , default_color_type, default_color_type&
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                    >
sl@0:           color_map(color_vec.begin(), color_vec.size(), index_map1);
sl@0:         record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
sl@0:         typedef color_traits<default_color_type> Color;
sl@0:         for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
sl@0:           if (color_map[*u] == Color::white()) {
sl@0:             dfs_visitor.start_vertex(*u, G1);
sl@0:             depth_first_visit(G1, *u, dfs_visitor, color_map);
sl@0:           }
sl@0:         }
sl@0:         // Create the dfs_num array and dfs_num_map
sl@0:         dfs_num_vec.resize(num_vertices(G1));
sl@0:         dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
sl@0:                                                   dfs_num_vec.size(), 
sl@0:                                                   index_map1
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                                   , dfs_num_vec.front()
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                                   );
sl@0:         size_type n = 0;
sl@0:         for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
sl@0:           dfs_num[*v] = n++;
sl@0:         
sl@0:         sort(ordered_edges, edge_cmp(G1, dfs_num));
sl@0:         
sl@0:     
sl@0:         int dfs_num_k = -1;
sl@0:         return this->match(ordered_edges.begin(), dfs_num_k);
sl@0:       }
sl@0:     
sl@0:     private:
sl@0:       bool match(edge_iter iter, int dfs_num_k)
sl@0:       {
sl@0:         if (iter != ordered_edges.end()) {
sl@0:           vertex1_t i = source(*iter, G1), j = target(*iter, G2);
sl@0:           if (dfs_num[i] > dfs_num_k) {
sl@0:             vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
sl@0:             BGL_FORALL_VERTICES_T(u, G2, Graph2) {
sl@0:               if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
sl@0:                 f[kp1] = u;
sl@0:                 in_S[u] = true;
sl@0:                 num_edges_on_k = 0;
sl@0:                 
sl@0:                 if (match(iter, dfs_num_k + 1))
sl@0: #if 0
sl@0:                     // dwa 2003/7/11 -- this *HAS* to be a bug!
sl@0:                     ;
sl@0: #endif 
sl@0:                     return true;
sl@0:                     
sl@0:                 in_S[u] = false;
sl@0:               }
sl@0:             }
sl@0:                
sl@0:           }
sl@0:           else if (dfs_num[j] > dfs_num_k) {
sl@0:             vertex1_t k = dfs_vertices[dfs_num_k];
sl@0:             num_edges_on_k -= 
sl@0:               count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));
sl@0:                 
sl@0:             for (int jj = 0; jj < dfs_num_k; ++jj) {
sl@0:               vertex1_t j = dfs_vertices[jj];
sl@0:               num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);
sl@0:             }
sl@0:                 
sl@0:             if (num_edges_on_k != 0)
sl@0:               return false;
sl@0:             BGL_FORALL_ADJ_T(f[i], v, G2, Graph2)
sl@0:               if (invariant2(v) == invariant1(j) && in_S[v] == false) {
sl@0:                 f[j] = v;
sl@0:                 in_S[v] = true;
sl@0:                 num_edges_on_k = 1;
sl@0:                 BOOST_USING_STD_MAX();
sl@0:                 int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));
sl@0:                 if (match(next(iter), next_k))
sl@0:                   return true;
sl@0:                 in_S[v] = false;
sl@0:               }
sl@0:                 
sl@0:                 
sl@0:           }
sl@0:           else {
sl@0:             if (contains(adjacent_vertices(f[i], G2), f[j])) {
sl@0:               ++num_edges_on_k;
sl@0:               if (match(next(iter), dfs_num_k))
sl@0:                 return true;
sl@0:             }
sl@0:                 
sl@0:           }
sl@0:         } else 
sl@0:           return true;
sl@0:         return false;
sl@0:       }
sl@0:     
sl@0:     };
sl@0: 
sl@0:     
sl@0:     template <typename Graph, typename InDegreeMap>
sl@0:     void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
sl@0:     {
sl@0:       BGL_FORALL_VERTICES_T(v, g, Graph)
sl@0:         put(in_degree_map, v, 0);
sl@0: 
sl@0:       BGL_FORALL_VERTICES_T(u, g, Graph)
sl@0:         BGL_FORALL_ADJ_T(u, v, g, Graph)
sl@0:         put(in_degree_map, v, get(in_degree_map, v) + 1);
sl@0:     }
sl@0: 
sl@0:   } // namespace detail
sl@0: 
sl@0: 
sl@0:   template <typename InDegreeMap, typename Graph>
sl@0:   class degree_vertex_invariant
sl@0:   {
sl@0:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
sl@0:     typedef typename graph_traits<Graph>::degree_size_type size_type;
sl@0:   public:
sl@0:     typedef vertex_t argument_type;
sl@0:     typedef size_type result_type;
sl@0: 
sl@0:     degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
sl@0:       : m_in_degree_map(in_degree_map), m_g(g) { }
sl@0: 
sl@0:     size_type operator()(vertex_t v) const {
sl@0:       return (num_vertices(m_g) + 1) * out_degree(v, m_g)
sl@0:         + get(m_in_degree_map, v);
sl@0:     }
sl@0:     // The largest possible vertex invariant number
sl@0:     size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { 
sl@0:       return num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g);
sl@0:     }
sl@0:   private:
sl@0:     InDegreeMap m_in_degree_map;
sl@0:     const Graph& m_g;
sl@0:   };
sl@0: 
sl@0: 
sl@0:   template <typename Graph1, typename Graph2, typename IsoMapping, 
sl@0:     typename Invariant1, typename Invariant2,
sl@0:     typename IndexMap1, typename IndexMap2>
sl@0:   bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, 
sl@0:                    Invariant1 invariant1, Invariant2 invariant2, 
sl@0:                    std::size_t max_invariant,
sl@0:                    IndexMap1 index_map1, IndexMap2 index_map2)
sl@0: 
sl@0:   {
sl@0:     // Graph requirements
sl@0:     function_requires< VertexListGraphConcept<Graph1> >();
sl@0:     function_requires< EdgeListGraphConcept<Graph1> >();
sl@0:     function_requires< VertexListGraphConcept<Graph2> >();
sl@0:     function_requires< BidirectionalGraphConcept<Graph2> >();
sl@0:     
sl@0:     typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
sl@0:     typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
sl@0:     typedef typename graph_traits<Graph1>::vertices_size_type size_type;
sl@0:     
sl@0:     // Vertex invariant requirement
sl@0:     function_requires< AdaptableUnaryFunctionConcept<Invariant1,
sl@0:       size_type, vertex1_t> >();
sl@0:     function_requires< AdaptableUnaryFunctionConcept<Invariant2,
sl@0:       size_type, vertex2_t> >();
sl@0:     
sl@0:     // Property map requirements
sl@0:     function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >();
sl@0:     typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
sl@0:     BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value));
sl@0:     
sl@0:     function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >();
sl@0:     typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
sl@0:     BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
sl@0:     
sl@0:     function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >();
sl@0:     typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
sl@0:     BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
sl@0:     
sl@0:     if (num_vertices(G1) != num_vertices(G2))
sl@0:       return false;
sl@0:     if (num_vertices(G1) == 0 && num_vertices(G2) == 0)
sl@0:       return true;
sl@0:     
sl@0:     detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
sl@0:       Invariant2, IndexMap1, IndexMap2> 
sl@0:       algo(G1, G2, f, invariant1, invariant2, max_invariant, 
sl@0:            index_map1, index_map2);
sl@0:     return algo.test_isomorphism();
sl@0:   }
sl@0: 
sl@0: 
sl@0:   namespace detail {
sl@0:   
sl@0:     template <typename Graph1, typename Graph2, 
sl@0:       typename IsoMapping, 
sl@0:       typename IndexMap1, typename IndexMap2,
sl@0:       typename P, typename T, typename R>
sl@0:     bool isomorphism_impl(const Graph1& G1, const Graph2& G2, 
sl@0:                           IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
sl@0:                           const bgl_named_params<P,T,R>& params)
sl@0:     {
sl@0:       std::vector<std::size_t> in_degree1_vec(num_vertices(G1));
sl@0:       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
sl@0:                                          IndexMap1
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                          , std::size_t, std::size_t&
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                          > InDeg1;
sl@0:       InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
sl@0:       compute_in_degree(G1, in_degree1);
sl@0: 
sl@0:       std::vector<std::size_t> in_degree2_vec(num_vertices(G2));
sl@0:       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, 
sl@0:                                          IndexMap2
sl@0: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
sl@0:                                          , std::size_t, std::size_t&
sl@0: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
sl@0:                                          > InDeg2;
sl@0:       InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
sl@0:       compute_in_degree(G2, in_degree2);
sl@0: 
sl@0:       degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);
sl@0:       degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);
sl@0: 
sl@0:       return isomorphism(G1, G2, f,
sl@0:                          choose_param(get_param(params, vertex_invariant1_t()), invariant1),
sl@0:                          choose_param(get_param(params, vertex_invariant2_t()), invariant2),
sl@0:                          choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),
sl@0:                          index_map1, index_map2
sl@0:                          );  
sl@0:     }  
sl@0:    
sl@0:   } // namespace detail
sl@0: 
sl@0: 
sl@0:   // Named parameter interface
sl@0:   template <typename Graph1, typename Graph2, class P, class T, class R>
sl@0:   bool isomorphism(const Graph1& g1,
sl@0:                    const Graph2& g2,
sl@0:                    const bgl_named_params<P,T,R>& params)
sl@0:   {
sl@0:     typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
sl@0:     typename std::vector<vertex2_t>::size_type n = num_vertices(g1);
sl@0:     std::vector<vertex2_t> f(n);
sl@0:     return detail::isomorphism_impl
sl@0:       (g1, g2, 
sl@0:        choose_param(get_param(params, vertex_isomorphism_t()),
sl@0:                     make_safe_iterator_property_map(f.begin(), f.size(),
sl@0:                                                     choose_const_pmap(get_param(params, vertex_index1),
sl@0:                                                                       g1, vertex_index), vertex2_t())),
sl@0:        choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index),
sl@0:        choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index),
sl@0:        params
sl@0:        );
sl@0:   }
sl@0: 
sl@0:   // All defaults interface
sl@0:   template <typename Graph1, typename Graph2>
sl@0:   bool isomorphism(const Graph1& g1, const Graph2& g2)
sl@0:   {
sl@0:     return isomorphism(g1, g2,
sl@0:                        bgl_named_params<int, buffer_param_t>(0));// bogus named param
sl@0:   }
sl@0: 
sl@0: 
sl@0:   // Verify that the given mapping iso_map from the vertices of g1 to the
sl@0:   // vertices of g2 describes an isomorphism.
sl@0:   // Note: this could be made much faster by specializing based on the graph
sl@0:   // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
sl@0:   // O(n^4) won't hurt us.
sl@0:   template<typename Graph1, typename Graph2, typename IsoMap>
sl@0:   inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)
sl@0:   {
sl@0: #if 0
sl@0:     // problematic for filtered_graph!
sl@0:     if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
sl@0:       return false;
sl@0: #endif
sl@0:   
sl@0:     for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first;
sl@0:          e1 != edges(g1).second; ++e1) {
sl@0:       bool found_edge = false;
sl@0:       for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first;
sl@0:            e2 != edges(g2).second && !found_edge; ++e2) {
sl@0:         if (source(*e2, g2) == get(iso_map, source(*e1, g1)) &&
sl@0:             target(*e2, g2) == get(iso_map, target(*e1, g1))) {
sl@0:           found_edge = true;
sl@0:         }
sl@0:       }
sl@0:     
sl@0:       if (!found_edge)
sl@0:         return false;
sl@0:     }
sl@0:   
sl@0:     return true;
sl@0:   }
sl@0: 
sl@0: } // namespace boost
sl@0: 
sl@0: #ifdef BOOST_ISO_INCLUDED_ITER_MACROS
sl@0: #undef BOOST_ISO_INCLUDED_ITER_MACROS
sl@0: #include <boost/graph/iteration_macros_undef.hpp>
sl@0: #endif
sl@0: 
sl@0: #endif // BOOST_GRAPH_ISOMORPHISM_HPP