1 // Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman

     2 //

     3 // Distributed under the Boost Software License, Version 1.0. (See

     4 // accompanying file LICENSE_1_0.txt or copy at

     5 // http://www.boost.org/LICENSE_1_0.txt)

     6 #ifndef BOOST_GRAPH_ISOMORPHISM_HPP

     7 #define BOOST_GRAPH_ISOMORPHISM_HPP

     8 

     9 #include <utility>

    10 #include <vector>

    11 #include <iterator>

    12 #include <algorithm>

    13 #include <boost/config.hpp>

    14 #include <boost/graph/depth_first_search.hpp>

    15 #include <boost/utility.hpp>

    16 #include <boost/detail/algorithm.hpp>

    17 #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap

    18 

    19 #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP

    20 #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file

    21 #include <boost/graph/iteration_macros.hpp>

    22 #endif

    23 

    24 namespace boost {

    25 

    26   namespace detail {

    27 

    28     template <typename Graph1, typename Graph2, typename IsoMapping,

    29       typename Invariant1, typename Invariant2,

    30       typename IndexMap1, typename IndexMap2>

    31     class isomorphism_algo

    32     {

    33       typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;

    34       typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

    35       typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;

    36       typedef typename graph_traits<Graph1>::vertices_size_type size_type;

    37       typedef typename Invariant1::result_type invar1_value;

    38       typedef typename Invariant2::result_type invar2_value;

    39     

    40       const Graph1& G1;

    41       const Graph2& G2;

    42       IsoMapping f;

    43       Invariant1 invariant1;

    44       Invariant2 invariant2;

    45       std::size_t max_invariant;

    46       IndexMap1 index_map1;

    47       IndexMap2 index_map2;

    48     

    49       std::vector<vertex1_t> dfs_vertices;

    50       typedef typename std::vector<vertex1_t>::iterator vertex_iter;

    51       std::vector<int> dfs_num_vec;

    52       typedef safe_iterator_property_map<typename std::vector<int>::iterator,

    53                                          IndexMap1

    54 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

    55                                          , int, int&

    56 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

    57                                          > DFSNumMap;

    58       DFSNumMap dfs_num;

    59       std::vector<edge1_t> ordered_edges;

    60       typedef typename std::vector<edge1_t>::iterator edge_iter;

    61     

    62       std::vector<char> in_S_vec;

    63       typedef safe_iterator_property_map<typename std::vector<char>::iterator,

    64                                          IndexMap2

    65 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

    66                                          , char, char&

    67 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

    68                                          > InSMap;

    69       InSMap in_S;

    70     

    71       int num_edges_on_k;

    72     

    73       friend struct compare_multiplicity;

    74       struct compare_multiplicity

    75       {

    76         compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)

    77           : invariant1(invariant1), multiplicity(multiplicity) { }

    78         bool operator()(const vertex1_t& x, const vertex1_t& y) const {

    79           return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];

    80         }

    81         Invariant1 invariant1;

    82         size_type* multiplicity;

    83       };

    84     

    85       struct record_dfs_order : default_dfs_visitor

    86       {

    87         record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 

    88           : vertices(v), edges(e) { }

    89     

    90         void discover_vertex(vertex1_t v, const Graph1&) const {

    91           vertices.push_back(v);

    92         }

    93         void examine_edge(edge1_t e, const Graph1& G1) const {

    94           edges.push_back(e);

    95         }

    96         std::vector<vertex1_t>& vertices;

    97         std::vector<edge1_t>& edges;

    98       };

    99     

   100       struct edge_cmp {

   101         edge_cmp(const Graph1& G1, DFSNumMap dfs_num)

   102           : G1(G1), dfs_num(dfs_num) { }

   103         bool operator()(const edge1_t& e1, const edge1_t& e2) const {

   104           using namespace std;

   105           int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];

   106           int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];

   107           int m1 = (max)(u1, v1);

   108           int m2 = (max)(u2, v2);

   109           // lexicographical comparison 

   110           return std::make_pair(m1, std::make_pair(u1, v1))

   111             < std::make_pair(m2, std::make_pair(u2, v2));

   112         }

   113         const Graph1& G1;

   114         DFSNumMap dfs_num;

   115       };

   116     

   117     public:

   118       isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,

   119                        Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,

   120                        IndexMap1 index_map1, IndexMap2 index_map2)

   121         : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),

   122           max_invariant(max_invariant),

   123           index_map1(index_map1), index_map2(index_map2)

   124       {

   125         in_S_vec.resize(num_vertices(G1));

   126         in_S = make_safe_iterator_property_map

   127           (in_S_vec.begin(), in_S_vec.size(), index_map2

   128 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

   129            , in_S_vec.front()

   130 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

   131            );

   132       }

   133     

   134       bool test_isomorphism()

   135       {

   136         {

   137           std::vector<invar1_value> invar1_array;

   138           BGL_FORALL_VERTICES_T(v, G1, Graph1)

   139             invar1_array.push_back(invariant1(v));

   140           sort(invar1_array);

   141         

   142           std::vector<invar2_value> invar2_array;

   143           BGL_FORALL_VERTICES_T(v, G2, Graph2)

   144             invar2_array.push_back(invariant2(v));

   145           sort(invar2_array);

   146           if (! equal(invar1_array, invar2_array))

   147             return false;

   148         }

   149         

   150         std::vector<vertex1_t> V_mult;

   151         BGL_FORALL_VERTICES_T(v, G1, Graph1)

   152           V_mult.push_back(v);

   153         {

   154           std::vector<size_type> multiplicity(max_invariant, 0);

   155           BGL_FORALL_VERTICES_T(v, G1, Graph1)

   156             ++multiplicity[invariant1(v)];

   157           sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));

   158         }

   159         

   160         std::vector<default_color_type> color_vec(num_vertices(G1));

   161         safe_iterator_property_map<std::vector<default_color_type>::iterator,

   162                                    IndexMap1

   163 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

   164                                    , default_color_type, default_color_type&

   165 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

   166                                    >

   167           color_map(color_vec.begin(), color_vec.size(), index_map1);

   168         record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);

   169         typedef color_traits<default_color_type> Color;

   170         for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {

   171           if (color_map[*u] == Color::white()) {

   172             dfs_visitor.start_vertex(*u, G1);

   173             depth_first_visit(G1, *u, dfs_visitor, color_map);

   174           }

   175         }

   176         // Create the dfs_num array and dfs_num_map

   177         dfs_num_vec.resize(num_vertices(G1));

   178         dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),

   179                                                   dfs_num_vec.size(), 

   180                                                   index_map1

   181 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

   182                                                   , dfs_num_vec.front()

   183 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

   184                                                   );

   185         size_type n = 0;

   186         for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)

   187           dfs_num[*v] = n++;

   188         

   189         sort(ordered_edges, edge_cmp(G1, dfs_num));

   190         

   191     

   192         int dfs_num_k = -1;

   193         return this->match(ordered_edges.begin(), dfs_num_k);

   194       }

   195     

   196     private:

   197       bool match(edge_iter iter, int dfs_num_k)

   198       {

   199         if (iter != ordered_edges.end()) {

   200           vertex1_t i = source(*iter, G1), j = target(*iter, G2);

   201           if (dfs_num[i] > dfs_num_k) {

   202             vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];

   203             BGL_FORALL_VERTICES_T(u, G2, Graph2) {

   204               if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {

   205                 f[kp1] = u;

   206                 in_S[u] = true;

   207                 num_edges_on_k = 0;

   208                 

   209                 if (match(iter, dfs_num_k + 1))

   210 #if 0

   211                     // dwa 2003/7/11 -- this *HAS* to be a bug!

   212                     ;

   213 #endif 

   214                     return true;

   215                     

   216                 in_S[u] = false;

   217               }

   218             }

   219                

   220           }

   221           else if (dfs_num[j] > dfs_num_k) {

   222             vertex1_t k = dfs_vertices[dfs_num_k];

   223             num_edges_on_k -= 

   224               count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));

   225                 

   226             for (int jj = 0; jj < dfs_num_k; ++jj) {

   227               vertex1_t j = dfs_vertices[jj];

   228               num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);

   229             }

   230                 

   231             if (num_edges_on_k != 0)

   232               return false;

   233             BGL_FORALL_ADJ_T(f[i], v, G2, Graph2)

   234               if (invariant2(v) == invariant1(j) && in_S[v] == false) {

   235                 f[j] = v;

   236                 in_S[v] = true;

   237                 num_edges_on_k = 1;

   238                 BOOST_USING_STD_MAX();

   239                 int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));

   240                 if (match(next(iter), next_k))

   241                   return true;

   242                 in_S[v] = false;

   243               }

   244                 

   245                 

   246           }

   247           else {

   248             if (contains(adjacent_vertices(f[i], G2), f[j])) {

   249               ++num_edges_on_k;

   250               if (match(next(iter), dfs_num_k))

   251                 return true;

   252             }

   253                 

   254           }

   255         } else 

   256           return true;

   257         return false;

   258       }

   259     

   260     };

   261 

   262     

   263     template <typename Graph, typename InDegreeMap>

   264     void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)

   265     {

   266       BGL_FORALL_VERTICES_T(v, g, Graph)

   267         put(in_degree_map, v, 0);

   268 

   269       BGL_FORALL_VERTICES_T(u, g, Graph)

   270         BGL_FORALL_ADJ_T(u, v, g, Graph)

   271         put(in_degree_map, v, get(in_degree_map, v) + 1);

   272     }

   273 

   274   } // namespace detail

   275 

   276 

   277   template <typename InDegreeMap, typename Graph>

   278   class degree_vertex_invariant

   279   {

   280     typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;

   281     typedef typename graph_traits<Graph>::degree_size_type size_type;

   282   public:

   283     typedef vertex_t argument_type;

   284     typedef size_type result_type;

   285 

   286     degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)

   287       : m_in_degree_map(in_degree_map), m_g(g) { }

   288 

   289     size_type operator()(vertex_t v) const {

   290       return (num_vertices(m_g) + 1) * out_degree(v, m_g)

   291         + get(m_in_degree_map, v);

   292     }

   293     // The largest possible vertex invariant number

   294     size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { 

   295       return num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g);

   296     }

   297   private:

   298     InDegreeMap m_in_degree_map;

   299     const Graph& m_g;

   300   };

   301 

   302 

   303   template <typename Graph1, typename Graph2, typename IsoMapping, 

   304     typename Invariant1, typename Invariant2,

   305     typename IndexMap1, typename IndexMap2>

   306   bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, 

   307                    Invariant1 invariant1, Invariant2 invariant2, 

   308                    std::size_t max_invariant,

   309                    IndexMap1 index_map1, IndexMap2 index_map2)

   310 

   311   {

   312     // Graph requirements

   313     function_requires< VertexListGraphConcept<Graph1> >();

   314     function_requires< EdgeListGraphConcept<Graph1> >();

   315     function_requires< VertexListGraphConcept<Graph2> >();

   316     function_requires< BidirectionalGraphConcept<Graph2> >();

   317     

   318     typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;

   319     typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

   320     typedef typename graph_traits<Graph1>::vertices_size_type size_type;

   321     

   322     // Vertex invariant requirement

   323     function_requires< AdaptableUnaryFunctionConcept<Invariant1,

   324       size_type, vertex1_t> >();

   325     function_requires< AdaptableUnaryFunctionConcept<Invariant2,

   326       size_type, vertex2_t> >();

   327     

   328     // Property map requirements

   329     function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >();

   330     typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;

   331     BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value));

   332     

   333     function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >();

   334     typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;

   335     BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));

   336     

   337     function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >();

   338     typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;

   339     BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));

   340     

   341     if (num_vertices(G1) != num_vertices(G2))

   342       return false;

   343     if (num_vertices(G1) == 0 && num_vertices(G2) == 0)

   344       return true;

   345     

   346     detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,

   347       Invariant2, IndexMap1, IndexMap2> 

   348       algo(G1, G2, f, invariant1, invariant2, max_invariant, 

   349            index_map1, index_map2);

   350     return algo.test_isomorphism();

   351   }

   352 

   353 

   354   namespace detail {

   355   

   356     template <typename Graph1, typename Graph2, 

   357       typename IsoMapping, 

   358       typename IndexMap1, typename IndexMap2,

   359       typename P, typename T, typename R>

   360     bool isomorphism_impl(const Graph1& G1, const Graph2& G2, 

   361                           IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,

   362                           const bgl_named_params<P,T,R>& params)

   363     {

   364       std::vector<std::size_t> in_degree1_vec(num_vertices(G1));

   365       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,

   366                                          IndexMap1

   367 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

   368                                          , std::size_t, std::size_t&

   369 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

   370                                          > InDeg1;

   371       InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);

   372       compute_in_degree(G1, in_degree1);

   373 

   374       std::vector<std::size_t> in_degree2_vec(num_vertices(G2));

   375       typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, 

   376                                          IndexMap2

   377 #ifdef BOOST_NO_STD_ITERATOR_TRAITS

   378                                          , std::size_t, std::size_t&

   379 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */

   380                                          > InDeg2;

   381       InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);

   382       compute_in_degree(G2, in_degree2);

   383 

   384       degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);

   385       degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);

   386 

   387       return isomorphism(G1, G2, f,

   388                          choose_param(get_param(params, vertex_invariant1_t()), invariant1),

   389                          choose_param(get_param(params, vertex_invariant2_t()), invariant2),

   390                          choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),

   391                          index_map1, index_map2

   392                          );  

   393     }  

   394    

   395   } // namespace detail

   396 

   397 

   398   // Named parameter interface

   399   template <typename Graph1, typename Graph2, class P, class T, class R>

   400   bool isomorphism(const Graph1& g1,

   401                    const Graph2& g2,

   402                    const bgl_named_params<P,T,R>& params)

   403   {

   404     typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

   405     typename std::vector<vertex2_t>::size_type n = num_vertices(g1);

   406     std::vector<vertex2_t> f(n);

   407     return detail::isomorphism_impl

   408       (g1, g2, 

   409        choose_param(get_param(params, vertex_isomorphism_t()),

   410                     make_safe_iterator_property_map(f.begin(), f.size(),

   411                                                     choose_const_pmap(get_param(params, vertex_index1),

   412                                                                       g1, vertex_index), vertex2_t())),

   413        choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index),

   414        choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index),

   415        params

   416        );

   417   }

   418 

   419   // All defaults interface

   420   template <typename Graph1, typename Graph2>

   421   bool isomorphism(const Graph1& g1, const Graph2& g2)

   422   {

   423     return isomorphism(g1, g2,

   424                        bgl_named_params<int, buffer_param_t>(0));// bogus named param

   425   }

   426 

   427 

   428   // Verify that the given mapping iso_map from the vertices of g1 to the

   429   // vertices of g2 describes an isomorphism.

   430   // Note: this could be made much faster by specializing based on the graph

   431   // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,

   432   // O(n^4) won't hurt us.

   433   template<typename Graph1, typename Graph2, typename IsoMap>

   434   inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)

   435   {

   436 #if 0

   437     // problematic for filtered_graph!

   438     if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))

   439       return false;

   440 #endif

   441   

   442     for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first;

   443          e1 != edges(g1).second; ++e1) {

   444       bool found_edge = false;

   445       for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first;

   446            e2 != edges(g2).second && !found_edge; ++e2) {

   447         if (source(*e2, g2) == get(iso_map, source(*e1, g1)) &&

   448             target(*e2, g2) == get(iso_map, target(*e1, g1))) {

   449           found_edge = true;

   450         }

   451       }

   452     

   453       if (!found_edge)

   454         return false;

   455     }

   456   

   457     return true;

   458   }

   459 

   460 } // namespace boost

   461 

   462 #ifdef BOOST_ISO_INCLUDED_ITER_MACROS

   463 #undef BOOST_ISO_INCLUDED_ITER_MACROS

   464 #include <boost/graph/iteration_macros_undef.hpp>

   465 #endif

   466 

   467 #endif // BOOST_GRAPH_ISOMORPHISM_HPP