Chris@16: // Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: #ifndef BOOST_GRAPH_ISOMORPHISM_HPP
Chris@16: #define BOOST_GRAPH_ISOMORPHISM_HPP
Chris@16: 
Chris@16: #include <utility>
Chris@16: #include <vector>
Chris@16: #include <iterator>
Chris@16: #include <algorithm>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/assert.hpp>
Chris@16: #include <boost/smart_ptr.hpp>
Chris@16: #include <boost/graph/depth_first_search.hpp>
Chris@16: #include <boost/detail/algorithm.hpp>
Chris@16: #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
Chris@16: #include <boost/concept/assert.hpp>
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
Chris@16: #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
Chris@16: #include <boost/graph/iteration_macros.hpp>
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   namespace detail {
Chris@16: 
Chris@16:     template <typename Graph1, typename Graph2, typename IsoMapping,
Chris@16:       typename Invariant1, typename Invariant2,
Chris@16:       typename IndexMap1, typename IndexMap2>
Chris@16:     class isomorphism_algo
Chris@16:     {
Chris@16:       typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
Chris@16:       typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
Chris@16:       typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
Chris@16:       typedef typename graph_traits<Graph1>::vertices_size_type size_type;
Chris@16:       typedef typename Invariant1::result_type invar1_value;
Chris@16:       typedef typename Invariant2::result_type invar2_value;
Chris@16:     
Chris@16:       const Graph1& G1;
Chris@16:       const Graph2& G2;
Chris@16:       IsoMapping f;
Chris@16:       Invariant1 invariant1;
Chris@16:       Invariant2 invariant2;
Chris@16:       std::size_t max_invariant;
Chris@16:       IndexMap1 index_map1;
Chris@16:       IndexMap2 index_map2;
Chris@16:     
Chris@16:       std::vector<vertex1_t> dfs_vertices;
Chris@16:       typedef typename std::vector<vertex1_t>::iterator vertex_iter;
Chris@16:       std::vector<int> dfs_num_vec;
Chris@16:       typedef safe_iterator_property_map<typename std::vector<int>::iterator,
Chris@16:                                          IndexMap1
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                          , int, int&
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                          > DFSNumMap;
Chris@16:       DFSNumMap dfs_num;
Chris@16:       std::vector<edge1_t> ordered_edges;
Chris@16:       typedef typename std::vector<edge1_t>::iterator edge_iter;
Chris@16:     
Chris@16:       std::vector<char> in_S_vec;
Chris@16:       typedef safe_iterator_property_map<typename std::vector<char>::iterator,
Chris@16:                                          IndexMap2
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                          , char, char&
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                          > InSMap;
Chris@16:       InSMap in_S;
Chris@16:     
Chris@16:       int num_edges_on_k;
Chris@16:     
Chris@16:       friend struct compare_multiplicity;
Chris@16:       struct compare_multiplicity
Chris@16:       {
Chris@16:         compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
Chris@16:           : invariant1(invariant1), multiplicity(multiplicity) { }
Chris@16:         bool operator()(const vertex1_t& x, const vertex1_t& y) const {
Chris@16:           return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
Chris@16:         }
Chris@16:         Invariant1 invariant1;
Chris@16:         size_type* multiplicity;
Chris@16:       };
Chris@16:     
Chris@16:       struct record_dfs_order : default_dfs_visitor
Chris@16:       {
Chris@16:         record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 
Chris@16:           : vertices(v), edges(e) { }
Chris@16:     
Chris@16:         void discover_vertex(vertex1_t v, const Graph1&) const {
Chris@16:           vertices.push_back(v);
Chris@16:         }
Chris@16:         void examine_edge(edge1_t e, const Graph1&) const {
Chris@16:           edges.push_back(e);
Chris@16:         }
Chris@16:         std::vector<vertex1_t>& vertices;
Chris@16:         std::vector<edge1_t>& edges;
Chris@16:       };
Chris@16:     
Chris@16:       struct edge_cmp {
Chris@16:         edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
Chris@16:           : G1(G1), dfs_num(dfs_num) { }
Chris@16:         bool operator()(const edge1_t& e1, const edge1_t& e2) const {
Chris@16:           using namespace std;
Chris@16:           int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
Chris@16:           int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
Chris@16:           int m1 = (max)(u1, v1);
Chris@16:           int m2 = (max)(u2, v2);
Chris@16:           // lexicographical comparison 
Chris@16:           return std::make_pair(m1, std::make_pair(u1, v1))
Chris@16:             < std::make_pair(m2, std::make_pair(u2, v2));
Chris@16:         }
Chris@16:         const Graph1& G1;
Chris@16:         DFSNumMap dfs_num;
Chris@16:       };
Chris@16:     
Chris@16:     public:
Chris@16:       isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
Chris@16:                        Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
Chris@16:                        IndexMap1 index_map1, IndexMap2 index_map2)
Chris@16:         : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
Chris@16:           max_invariant(max_invariant),
Chris@16:           index_map1(index_map1), index_map2(index_map2)
Chris@16:       {
Chris@16:         in_S_vec.resize(num_vertices(G1));
Chris@16:         in_S = make_safe_iterator_property_map
Chris@16:           (in_S_vec.begin(), in_S_vec.size(), index_map2
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:            , in_S_vec.front()
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:            );
Chris@16:       }
Chris@16:     
Chris@16:       bool test_isomorphism()
Chris@16:       {
Chris@16:         // reset isomapping
Chris@16:         BGL_FORALL_VERTICES_T(v, G1, Graph1)
Chris@16:           f[v] = graph_traits<Graph2>::null_vertex();
Chris@16:           
Chris@16:         {
Chris@16:           std::vector<invar1_value> invar1_array;
Chris@16:           BGL_FORALL_VERTICES_T(v, G1, Graph1)
Chris@16:             invar1_array.push_back(invariant1(v));
Chris@16:           sort(invar1_array);
Chris@16:         
Chris@16:           std::vector<invar2_value> invar2_array;
Chris@16:           BGL_FORALL_VERTICES_T(v, G2, Graph2)
Chris@16:             invar2_array.push_back(invariant2(v));
Chris@16:           sort(invar2_array);
Chris@16:           if (! equal(invar1_array, invar2_array))
Chris@16:             return false;
Chris@16:         }
Chris@16:         
Chris@16:         std::vector<vertex1_t> V_mult;
Chris@16:         BGL_FORALL_VERTICES_T(v, G1, Graph1)
Chris@16:           V_mult.push_back(v);
Chris@16:         {
Chris@16:           std::vector<size_type> multiplicity(max_invariant, 0);
Chris@16:           BGL_FORALL_VERTICES_T(v, G1, Graph1)
Chris@16:             ++multiplicity.at(invariant1(v));
Chris@16:           sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
Chris@16:         }
Chris@16:         
Chris@16:         std::vector<default_color_type> color_vec(num_vertices(G1));
Chris@16:         safe_iterator_property_map<std::vector<default_color_type>::iterator,
Chris@16:                                    IndexMap1
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                    , default_color_type, default_color_type&
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                    >
Chris@16:           color_map(color_vec.begin(), color_vec.size(), index_map1);
Chris@16:         record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
Chris@16:         typedef color_traits<default_color_type> Color;
Chris@16:         for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
Chris@16:           if (color_map[*u] == Color::white()) {
Chris@16:             dfs_visitor.start_vertex(*u, G1);
Chris@16:             depth_first_visit(G1, *u, dfs_visitor, color_map);
Chris@16:           }
Chris@16:         }
Chris@16:         // Create the dfs_num array and dfs_num_map
Chris@16:         dfs_num_vec.resize(num_vertices(G1));
Chris@16:         dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
Chris@16:                                                   dfs_num_vec.size(), 
Chris@16:                                                   index_map1
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                                   , dfs_num_vec.front()
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                                   );
Chris@16:         size_type n = 0;
Chris@16:         for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
Chris@16:           dfs_num[*v] = n++;
Chris@16:         
Chris@16:         sort(ordered_edges, edge_cmp(G1, dfs_num));
Chris@16:         
Chris@16:     
Chris@16:         int dfs_num_k = -1;
Chris@16:         return this->match(ordered_edges.begin(), dfs_num_k);
Chris@16:       }
Chris@16:     
Chris@16:     private:
Chris@16:       struct match_continuation {
Chris@16:         enum {pos_G2_vertex_loop, pos_fi_adj_loop, pos_dfs_num} position;
Chris@16:         typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
Chris@16:         std::pair<vertex_iterator, vertex_iterator> G2_verts;
Chris@16:         typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
Chris@16:         std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
Chris@16:         edge_iter iter;
Chris@16:         int dfs_num_k;
Chris@16:       };
Chris@16: 
Chris@16:       bool match(edge_iter iter, int dfs_num_k)
Chris@16:       {
Chris@16:         std::vector<match_continuation> k;
Chris@16:         typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
Chris@16:         std::pair<vertex_iterator, vertex_iterator> G2_verts(vertices(G2));
Chris@16:         typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
Chris@16:         std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
Chris@16:         vertex1_t i, j;
Chris@16: 
Chris@16:         recur:
Chris@16:         if (iter != ordered_edges.end()) {
Chris@16:           i = source(*iter, G1);
Chris@16:           j = target(*iter, G1);
Chris@16:           if (dfs_num[i] > dfs_num_k) {
Chris@16:             G2_verts = vertices(G2);
Chris@16:             while (G2_verts.first != G2_verts.second) {
Chris@16:               {
Chris@16:                 vertex2_t u = *G2_verts.first;
Chris@16:                 vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
Chris@16:                 if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
Chris@16:                   {
Chris@16:                     f[kp1] = u;
Chris@16:                     in_S[u] = true;
Chris@16:                     num_edges_on_k = 0;
Chris@16:                     
Chris@16:                     match_continuation new_k;
Chris@16:                     new_k.position = match_continuation::pos_G2_vertex_loop;
Chris@16:                     new_k.G2_verts = G2_verts;
Chris@16:                     new_k.iter = iter;
Chris@16:                     new_k.dfs_num_k = dfs_num_k;
Chris@16:                     k.push_back(new_k);
Chris@16:                     ++dfs_num_k;
Chris@16:                     goto recur;
Chris@16:                   }
Chris@16:                 }
Chris@16:               }
Chris@16: G2_loop_k:    ++G2_verts.first;
Chris@16:             }
Chris@16:                
Chris@16:           }
Chris@16:           else if (dfs_num[j] > dfs_num_k) {
Chris@16:             {
Chris@16:               vertex1_t vk = dfs_vertices[dfs_num_k];
Chris@16:               num_edges_on_k -= 
Chris@16:                 count_if(adjacent_vertices(f[vk], G2), make_indirect_pmap(in_S));
Chris@16:                   
Chris@16:               for (int jj = 0; jj < dfs_num_k; ++jj) {
Chris@16:                 vertex1_t j = dfs_vertices[jj];
Chris@16:                 num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[vk]);
Chris@16:               }
Chris@16:             }
Chris@16:                 
Chris@16:             if (num_edges_on_k != 0)
Chris@16:               goto return_point_false;
Chris@16:             fi_adj = adjacent_vertices(f[i], G2);
Chris@16:             while (fi_adj.first != fi_adj.second) {
Chris@16:               {
Chris@16:                 vertex2_t v = *fi_adj.first;
Chris@16:                 if (invariant2(v) == invariant1(j) && in_S[v] == false) {
Chris@16:                   f[j] = v;
Chris@16:                   in_S[v] = true;
Chris@16:                   num_edges_on_k = 1;
Chris@16:                   BOOST_USING_STD_MAX();
Chris@16:                   int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));
Chris@16:                   match_continuation new_k;
Chris@16:                   new_k.position = match_continuation::pos_fi_adj_loop;
Chris@16:                   new_k.fi_adj = fi_adj;
Chris@16:                   new_k.iter = iter;
Chris@16:                   new_k.dfs_num_k = dfs_num_k;
Chris@16:                   ++iter;
Chris@16:                   dfs_num_k = next_k;
Chris@16:                   k.push_back(new_k);
Chris@16:                   goto recur;
Chris@16:                 }
Chris@16:               }
Chris@16: fi_adj_loop_k:++fi_adj.first;
Chris@16:             }
Chris@16:           }
Chris@16:           else {
Chris@16:             if (container_contains(adjacent_vertices(f[i], G2), f[j])) {
Chris@16:               ++num_edges_on_k;
Chris@16:               match_continuation new_k;
Chris@16:               new_k.position = match_continuation::pos_dfs_num;
Chris@16:               k.push_back(new_k);
Chris@16:               ++iter;
Chris@16:               goto recur;
Chris@16:             }
Chris@16:                 
Chris@16:           }
Chris@16:         } else 
Chris@16:           goto return_point_true;
Chris@16:         goto return_point_false;
Chris@16:     
Chris@16:         {
Chris@16:           return_point_true: return true;
Chris@16: 
Chris@16:           return_point_false:
Chris@16:           if (k.empty()) return false;
Chris@16:           const match_continuation& this_k = k.back();
Chris@16:           switch (this_k.position) {
Chris@16:             case match_continuation::pos_G2_vertex_loop: {G2_verts = this_k.G2_verts; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*G2_verts.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto G2_loop_k;}
Chris@16:             case match_continuation::pos_fi_adj_loop: {fi_adj = this_k.fi_adj; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*fi_adj.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto fi_adj_loop_k;}
Chris@16:             case match_continuation::pos_dfs_num: {k.pop_back(); goto return_point_false;}
Chris@16:             default: {
Chris@16:               BOOST_ASSERT(!"Bad position");
Chris@16: #ifdef UNDER_CE
Chris@16:               exit(-1);
Chris@16: #else
Chris@16:               abort();
Chris@16: #endif
Chris@16:             }
Chris@16:           }
Chris@16:         }
Chris@16:       }
Chris@16:     };
Chris@16: 
Chris@16:     
Chris@16:     template <typename Graph, typename InDegreeMap>
Chris@16:     void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
Chris@16:     {
Chris@16:       BGL_FORALL_VERTICES_T(v, g, Graph)
Chris@16:         put(in_degree_map, v, 0);
Chris@16: 
Chris@16:       BGL_FORALL_VERTICES_T(u, g, Graph)
Chris@16:         BGL_FORALL_ADJ_T(u, v, g, Graph)
Chris@16:         put(in_degree_map, v, get(in_degree_map, v) + 1);
Chris@16:     }
Chris@16: 
Chris@16:   } // namespace detail
Chris@16: 
Chris@16: 
Chris@16:   template <typename InDegreeMap, typename Graph>
Chris@16:   class degree_vertex_invariant
Chris@16:   {
Chris@16:     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
Chris@16:     typedef typename graph_traits<Graph>::degree_size_type size_type;
Chris@16:   public:
Chris@16:     typedef vertex_t argument_type;
Chris@16:     typedef size_type result_type;
Chris@16: 
Chris@16:     degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
Chris@16:       : m_in_degree_map(in_degree_map),
Chris@16:         m_max_vertex_in_degree(0),
Chris@16:         m_max_vertex_out_degree(0),
Chris@16:         m_g(g) {
Chris@16:       BGL_FORALL_VERTICES_T(v, g, Graph) {
Chris@16:         m_max_vertex_in_degree =
Chris@16:           (std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v));
Chris@16:         m_max_vertex_out_degree =
Chris@16:           (std::max)(m_max_vertex_out_degree, out_degree(v, g));
Chris@16:       }
Chris@16:     }
Chris@16: 
Chris@16:     size_type operator()(vertex_t v) const {
Chris@16:       return (m_max_vertex_in_degree + 1) * out_degree(v, m_g)
Chris@16:         + get(m_in_degree_map, v);
Chris@16:     }
Chris@16:     // The largest possible vertex invariant number
Chris@16:     size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { 
Chris@16:       return (m_max_vertex_in_degree + 1) * (m_max_vertex_out_degree + 1);
Chris@16:     }
Chris@16:   private:
Chris@16:     InDegreeMap m_in_degree_map;
Chris@16:     size_type m_max_vertex_in_degree;
Chris@16:     size_type m_max_vertex_out_degree;
Chris@16:     const Graph& m_g;
Chris@16:   };
Chris@16: 
Chris@16:   // Count actual number of vertices, even in filtered graphs.
Chris@16:   template <typename Graph>
Chris@16:   size_t count_vertices(const Graph& g)
Chris@16:   {
Chris@16:       size_t n = 0;
Chris@16:       BGL_FORALL_VERTICES_T(v, g, Graph) {(void)v; ++n;}
Chris@16:       return n;
Chris@16:   }
Chris@16: 
Chris@16:   template <typename Graph1, typename Graph2, typename IsoMapping, 
Chris@16:     typename Invariant1, typename Invariant2,
Chris@16:     typename IndexMap1, typename IndexMap2>
Chris@16:   bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, 
Chris@16:                    Invariant1 invariant1, Invariant2 invariant2, 
Chris@16:                    std::size_t max_invariant,
Chris@16:                    IndexMap1 index_map1, IndexMap2 index_map2)
Chris@16: 
Chris@16:   {
Chris@16:     // Graph requirements
Chris@16:     BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph1> ));
Chris@16:     BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph1> ));
Chris@16:     BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph2> ));
Chris@16:     //BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph2> ));
Chris@16:     
Chris@16:     typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
Chris@16:     typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
Chris@16:     typedef typename graph_traits<Graph1>::vertices_size_type size_type;
Chris@16:     
Chris@16:     // Vertex invariant requirement
Chris@16:     BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant1,
Chris@16:       size_type, vertex1_t> ));
Chris@16:     BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant2,
Chris@16:       size_type, vertex2_t> ));
Chris@16:     
Chris@16:     // Property map requirements
Chris@16:     BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<IsoMapping, vertex1_t> ));
Chris@16:     typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
Chris@16:     BOOST_STATIC_ASSERT((is_convertible<IsoMappingValue, vertex2_t>::value));
Chris@16:     
Chris@16:     BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap1, vertex1_t> ));
Chris@16:     typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
Chris@16:     BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
Chris@16:     
Chris@16:     BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap2, vertex2_t> ));
Chris@16:     typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
Chris@16:     BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
Chris@16:     
Chris@16:     if (count_vertices(G1) != count_vertices(G2))
Chris@16:       return false;
Chris@16:     if (count_vertices(G1) == 0 && count_vertices(G2) == 0)
Chris@16:       return true;
Chris@16:     
Chris@16:     detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
Chris@16:       Invariant2, IndexMap1, IndexMap2> 
Chris@16:       algo(G1, G2, f, invariant1, invariant2, max_invariant, 
Chris@16:            index_map1, index_map2);
Chris@16:     return algo.test_isomorphism();
Chris@16:   }
Chris@16: 
Chris@16: 
Chris@16:   namespace detail {
Chris@16:   
Chris@16:     template <typename Graph1, typename Graph2, 
Chris@16:       typename IsoMapping, 
Chris@16:       typename IndexMap1, typename IndexMap2,
Chris@16:       typename P, typename T, typename R>
Chris@16:     bool isomorphism_impl(const Graph1& G1, const Graph2& G2, 
Chris@16:                           IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
Chris@16:                           const bgl_named_params<P,T,R>& params)
Chris@16:     {
Chris@16:       std::vector<std::size_t> in_degree1_vec(num_vertices(G1));
Chris@16:       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
Chris@16:                                          IndexMap1
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                          , std::size_t, std::size_t&
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                          > InDeg1;
Chris@16:       InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
Chris@16:       compute_in_degree(G1, in_degree1);
Chris@16: 
Chris@16:       std::vector<std::size_t> in_degree2_vec(num_vertices(G2));
Chris@16:       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, 
Chris@16:                                          IndexMap2
Chris@16: #ifdef BOOST_NO_STD_ITERATOR_TRAITS
Chris@16:                                          , std::size_t, std::size_t&
Chris@16: #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
Chris@16:                                          > InDeg2;
Chris@16:       InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
Chris@16:       compute_in_degree(G2, in_degree2);
Chris@16: 
Chris@16:       degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);
Chris@16:       degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);
Chris@16: 
Chris@16:       return isomorphism(G1, G2, f,
Chris@16:                          choose_param(get_param(params, vertex_invariant1_t()), invariant1),
Chris@16:                          choose_param(get_param(params, vertex_invariant2_t()), invariant2),
Chris@16:                          choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),
Chris@16:                          index_map1, index_map2
Chris@16:                          );  
Chris@16:     }  
Chris@16: 
Chris@16:     template <typename G, typename Index>
Chris@16:     struct make_degree_invariant {
Chris@16:       const G& g;
Chris@16:       const Index& index;
Chris@16:       make_degree_invariant(const G& g, const Index& index): g(g), index(index) {}
Chris@16:       typedef typename boost::graph_traits<G>::degree_size_type degree_size_type;
Chris@16:       typedef shared_array_property_map<degree_size_type, Index> prop_map_type;
Chris@16:       typedef degree_vertex_invariant<prop_map_type, G> result_type;
Chris@16:       result_type operator()() const {
Chris@16:         prop_map_type pm = make_shared_array_property_map(num_vertices(g), degree_size_type(), index);
Chris@16:         compute_in_degree(g, pm);
Chris@16:         return result_type(pm, g);
Chris@16:       }
Chris@16:     };
Chris@16:    
Chris@16:   } // namespace detail
Chris@16: 
Chris@16:   namespace graph {
Chris@16:     namespace detail {
Chris@16:       template <typename Graph1, typename Graph2>
Chris@16:       struct isomorphism_impl {
Chris@16:         typedef bool result_type;
Chris@16:         template <typename ArgPack>
Chris@16:         bool operator()(const Graph1& g1, const Graph2& g2, const ArgPack& arg_pack) const {
Chris@16:           using namespace boost::graph::keywords;
Chris@16:           typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index1_map, boost::vertex_index_t, Graph1>::type index1_map_type;
Chris@16:           typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index2_map, boost::vertex_index_t, Graph2>::type index2_map_type;
Chris@16:           index1_map_type index1_map = boost::detail::override_const_property(arg_pack, _vertex_index1_map, g1, boost::vertex_index);
Chris@16:           index2_map_type index2_map = boost::detail::override_const_property(arg_pack, _vertex_index2_map, g2, boost::vertex_index);
Chris@16:           typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
Chris@16:           typename std::vector<vertex2_t>::size_type n = (typename std::vector<vertex2_t>::size_type)num_vertices(g1);
Chris@16:           std::vector<vertex2_t> f(n);
Chris@16:           typename boost::parameter::lazy_binding<
Chris@16:                      ArgPack,
Chris@16:                      tag::vertex_invariant1,
Chris@16:                      boost::detail::make_degree_invariant<Graph1, index1_map_type> >::type
Chris@16:             invariant1 =
Chris@16:               arg_pack[_vertex_invariant1 || boost::detail::make_degree_invariant<Graph1, index1_map_type>(g1, index1_map)];
Chris@16:           typename boost::parameter::lazy_binding<
Chris@16:                      ArgPack,
Chris@16:                      tag::vertex_invariant2,
Chris@16:                      boost::detail::make_degree_invariant<Graph2, index2_map_type> >::type
Chris@16:             invariant2 =
Chris@16:               arg_pack[_vertex_invariant2 || boost::detail::make_degree_invariant<Graph2, index2_map_type>(g2, index2_map)];
Chris@16:           return boost::isomorphism
Chris@16:                    (g1, g2,
Chris@16:                     choose_param(arg_pack[_isomorphism_map | boost::param_not_found()],
Chris@16:                                  make_shared_array_property_map(num_vertices(g1), vertex2_t(), index1_map)),
Chris@16:                     invariant1,
Chris@16:                     invariant2,
Chris@16:                     arg_pack[_vertex_max_invariant | (invariant2.max)()],
Chris@16:                     index1_map,
Chris@16:                     index2_map);
Chris@16:         }
Chris@16:       };
Chris@16:     }
Chris@16:     BOOST_GRAPH_MAKE_FORWARDING_FUNCTION(isomorphism, 2, 6)
Chris@16:   }
Chris@16: 
Chris@16:   // Named parameter interface
Chris@16:   BOOST_GRAPH_MAKE_OLD_STYLE_PARAMETER_FUNCTION(isomorphism, 2)
Chris@16: 
Chris@16:   // Verify that the given mapping iso_map from the vertices of g1 to the
Chris@16:   // vertices of g2 describes an isomorphism.
Chris@16:   // Note: this could be made much faster by specializing based on the graph
Chris@16:   // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
Chris@16:   // O(n^4) won't hurt us.
Chris@16:   template<typename Graph1, typename Graph2, typename IsoMap>
Chris@16:   inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)
Chris@16:   {
Chris@16: #if 0
Chris@16:     // problematic for filtered_graph!
Chris@16:     if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
Chris@16:       return false;
Chris@16: #endif
Chris@16:   
Chris@16:     BGL_FORALL_EDGES_T(e1, g1, Graph1) {
Chris@16:       bool found_edge = false;
Chris@16:       BGL_FORALL_EDGES_T(e2, g2, Graph2) {
Chris@16:         if (source(e2, g2) == get(iso_map, source(e1, g1)) &&
Chris@16:             target(e2, g2) == get(iso_map, target(e1, g1))) {
Chris@16:           found_edge = true;
Chris@16:         }
Chris@16:       }
Chris@16:     
Chris@16:       if (!found_edge)
Chris@16:         return false;
Chris@16:     }
Chris@16:   
Chris@16:     return true;
Chris@16:   }
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #ifdef BOOST_ISO_INCLUDED_ITER_MACROS
Chris@16: #undef BOOST_ISO_INCLUDED_ITER_MACROS
Chris@16: #include <boost/graph/iteration_macros_undef.hpp>
Chris@16: #endif
Chris@16: 
Chris@16: #endif // BOOST_GRAPH_ISOMORPHISM_HPP