epoc32/include/stdapis/boost/graph/isomorphism.hpp
author William Roberts <williamr@symbian.org>
Wed, 31 Mar 2010 12:33:34 +0100
branchSymbian3
changeset 4 837f303aceeb
permissions -rw-r--r--
Current Symbian^3 public API header files (from PDK 3.0.h)
This is the epoc32/include tree with the "platform" subtrees removed, and
all but a selected few mbg and rsg files removed.
     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