ceph/src/boost/boost/graph/isomorphism.hpp

   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/assert.hpp>
  15 #include <boost/smart_ptr.hpp>
  16 #include <boost/graph/depth_first_search.hpp>
  17 #include <boost/detail/algorithm.hpp>
  18 #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
  19 #include <boost/concept/assert.hpp>
  20
  21 #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
  22 #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
  23 #include <boost/graph/iteration_macros.hpp>
  24 #endif
  25
  26 namespace boost
  27 {
  28
  29 namespace detail
  30 {
  31
  32     template < typename Graph1, typename Graph2, typename IsoMapping,
  33         typename Invariant1, typename Invariant2, typename IndexMap1,
  34         typename IndexMap2 >
  35     class isomorphism_algo
  36     {
  37         typedef typename graph_traits< Graph1 >::vertex_descriptor vertex1_t;
  38         typedef typename graph_traits< Graph2 >::vertex_descriptor vertex2_t;
  39         typedef typename graph_traits< Graph1 >::edge_descriptor edge1_t;
  40         typedef typename graph_traits< Graph1 >::vertices_size_type size_type;
  41         typedef typename Invariant1::result_type invar1_value;
  42         typedef typename Invariant2::result_type invar2_value;
  43
  44         const Graph1& G1;
  45         const Graph2& G2;
  46         IsoMapping f;
  47         Invariant1 invariant1;
  48         Invariant2 invariant2;
  49         std::size_t max_invariant;
  50         IndexMap1 index_map1;
  51         IndexMap2 index_map2;
  52
  53         std::vector< vertex1_t > dfs_vertices;
  54         typedef typename std::vector< vertex1_t >::iterator vertex_iter;
  55         std::vector< int > dfs_num_vec;
  56         typedef safe_iterator_property_map<
  57             typename std::vector< int >::iterator, IndexMap1
  58 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
  59             ,
  60             int, int&
  61 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
  62             >
  63             DFSNumMap;
  64         DFSNumMap dfs_num;
  65         std::vector< edge1_t > ordered_edges;
  66         typedef typename std::vector< edge1_t >::iterator edge_iter;
  67
  68         std::vector< char > in_S_vec;
  69         typedef safe_iterator_property_map<
  70             typename std::vector< char >::iterator, IndexMap2
  71 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
  72             ,
  73             char, char&
  74 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
  75             >
  76             InSMap;
  77         InSMap in_S;
  78
  79         int num_edges_on_k;
  80
  81         friend struct compare_multiplicity;
  82         struct compare_multiplicity
  83         {
  84             compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
  85             : invariant1(invariant1), multiplicity(multiplicity)
  86             {
  87             }
  88             bool operator()(const vertex1_t& x, const vertex1_t& y) const
  89             {
  90                 return multiplicity[invariant1(x)]
  91                     < multiplicity[invariant1(y)];
  92             }
  93             Invariant1 invariant1;
  94             size_type* multiplicity;
  95         };
  96
  97         struct record_dfs_order : default_dfs_visitor
  98         {
  99             record_dfs_order(
 100                 std::vector< vertex1_t >& v, std::vector< edge1_t >& e)
 101             : vertices(v), edges(e)
 102             {
 103             }
 104
 105             void discover_vertex(vertex1_t v, const Graph1&) const
 106             {
 107                 vertices.push_back(v);
 108             }
 109             void examine_edge(edge1_t e, const Graph1&) const
 110             {
 111                 edges.push_back(e);
 112             }
 113             std::vector< vertex1_t >& vertices;
 114             std::vector< edge1_t >& edges;
 115         };
 116
 117         struct edge_cmp
 118         {
 119             edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
 120             : G1(G1), dfs_num(dfs_num)
 121             {
 122             }
 123             bool operator()(const edge1_t& e1, const edge1_t& e2) const
 124             {
 125                 using namespace std;
 126                 int u1 = dfs_num[source(e1, G1)], v1 = dfs_num[target(e1, G1)];
 127                 int u2 = dfs_num[source(e2, G1)], v2 = dfs_num[target(e2, G1)];
 128                 int m1 = (max)(u1, v1);
 129                 int m2 = (max)(u2, v2);
 130                 // lexicographical comparison
 131                 return std::make_pair(m1, std::make_pair(u1, v1))
 132                     < std::make_pair(m2, std::make_pair(u2, v2));
 133             }
 134             const Graph1& G1;
 135             DFSNumMap dfs_num;
 136         };
 137
 138     public:
 139         isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
 140             Invariant1 invariant1, Invariant2 invariant2,
 141             std::size_t max_invariant, IndexMap1 index_map1,
 142             IndexMap2 index_map2)
 143         : G1(G1)
 144         , G2(G2)
 145         , f(f)
 146         , invariant1(invariant1)
 147         , invariant2(invariant2)
 148         , max_invariant(max_invariant)
 149         , index_map1(index_map1)
 150         , index_map2(index_map2)
 151         {
 152             in_S_vec.resize(num_vertices(G1));
 153             in_S = make_safe_iterator_property_map(
 154                 in_S_vec.begin(), in_S_vec.size(), index_map2
 155 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
 156                 ,
 157                 in_S_vec.front()
 158 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
 159             );
 160         }
 161
 162         bool test_isomorphism()
 163         {
 164             // reset isomapping
 165             BGL_FORALL_VERTICES_T(v, G1, Graph1)
 166             f[v] = graph_traits< Graph2 >::null_vertex();
 167
 168             {
 169                 std::vector< invar1_value > invar1_array;
 170                 BGL_FORALL_VERTICES_T(v, G1, Graph1)
 171                 invar1_array.push_back(invariant1(v));
 172                 sort(invar1_array);
 173
 174                 std::vector< invar2_value > invar2_array;
 175                 BGL_FORALL_VERTICES_T(v, G2, Graph2)
 176                 invar2_array.push_back(invariant2(v));
 177                 sort(invar2_array);
 178                 if (!equal(invar1_array, invar2_array))
 179                     return false;
 180             }
 181
 182             std::vector< vertex1_t > V_mult;
 183             BGL_FORALL_VERTICES_T(v, G1, Graph1)
 184             V_mult.push_back(v);
 185             {
 186                 std::vector< size_type > multiplicity(max_invariant, 0);
 187                 BGL_FORALL_VERTICES_T(v, G1, Graph1)
 188                 ++multiplicity.at(invariant1(v));
 189                 sort(
 190                     V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
 191             }
 192
 193             std::vector< default_color_type > color_vec(num_vertices(G1));
 194             safe_iterator_property_map<
 195                 std::vector< default_color_type >::iterator, IndexMap1
 196 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
 197                 ,
 198                 default_color_type, default_color_type&
 199 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
 200                 >
 201                 color_map(color_vec.begin(), color_vec.size(), index_map1);
 202             record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
 203             typedef color_traits< default_color_type > Color;
 204             for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u)
 205             {
 206                 if (color_map[*u] == Color::white())
 207                 {
 208                     dfs_visitor.start_vertex(*u, G1);
 209                     depth_first_visit(G1, *u, dfs_visitor, color_map);
 210                 }
 211             }
 212             // Create the dfs_num array and dfs_num_map
 213             dfs_num_vec.resize(num_vertices(G1));
 214             dfs_num = make_safe_iterator_property_map(
 215                 dfs_num_vec.begin(), dfs_num_vec.size(), index_map1
 216 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
 217                 ,
 218                 dfs_num_vec.front()
 219 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
 220             );
 221             size_type n = 0;
 222             for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end();
 223                  ++v)
 224                 dfs_num[*v] = n++;
 225
 226             sort(ordered_edges, edge_cmp(G1, dfs_num));
 227
 228             int dfs_num_k = -1;
 229             return this->match(ordered_edges.begin(), dfs_num_k);
 230         }
 231
 232     private:
 233         struct match_continuation
 234         {
 235             enum
 236             {
 237                 pos_G2_vertex_loop,
 238                 pos_fi_adj_loop,
 239                 pos_dfs_num
 240             } position;
 241             typedef typename graph_traits< Graph2 >::vertex_iterator
 242                 vertex_iterator;
 243             std::pair< vertex_iterator, vertex_iterator > G2_verts;
 244             typedef typename graph_traits< Graph2 >::adjacency_iterator
 245                 adjacency_iterator;
 246             std::pair< adjacency_iterator, adjacency_iterator > fi_adj;
 247             edge_iter iter;
 248             int dfs_num_k;
 249         };
 250
 251         bool match(edge_iter iter, int dfs_num_k)
 252         {
 253             std::vector< match_continuation > k;
 254             typedef typename graph_traits< Graph2 >::vertex_iterator
 255                 vertex_iterator;
 256             std::pair< vertex_iterator, vertex_iterator > G2_verts(
 257                 vertices(G2));
 258             typedef typename graph_traits< Graph2 >::adjacency_iterator
 259                 adjacency_iterator;
 260             std::pair< adjacency_iterator, adjacency_iterator > fi_adj;
 261             vertex1_t i, j;
 262
 263         recur:
 264             if (iter != ordered_edges.end())
 265             {
 266                 i = source(*iter, G1);
 267                 j = target(*iter, G1);
 268                 if (dfs_num[i] > dfs_num_k)
 269                 {
 270                     G2_verts = vertices(G2);
 271                     while (G2_verts.first != G2_verts.second)
 272                     {
 273                         {
 274                             vertex2_t u = *G2_verts.first;
 275                             vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
 276                             if (invariant1(kp1) == invariant2(u)
 277                                 && in_S[u] == false)
 278                             {
 279                                 {
 280                                     f[kp1] = u;
 281                                     in_S[u] = true;
 282                                     num_edges_on_k = 0;
 283
 284                                     match_continuation new_k;
 285                                     new_k.position = match_continuation::
 286                                         pos_G2_vertex_loop;
 287                                     new_k.G2_verts = G2_verts;
 288                                     new_k.iter = iter;
 289                                     new_k.dfs_num_k = dfs_num_k;
 290                                     k.push_back(new_k);
 291                                     ++dfs_num_k;
 292                                     goto recur;
 293                                 }
 294                             }
 295                         }
 296                     G2_loop_k:
 297                         ++G2_verts.first;
 298                     }
 299                 }
 300                 else if (dfs_num[j] > dfs_num_k)
 301                 {
 302                     {
 303                         vertex1_t vk = dfs_vertices[dfs_num_k];
 304                         num_edges_on_k -= count_if(adjacent_vertices(f[vk], G2),
 305                             make_indirect_pmap(in_S));
 306
 307                         for (int jj = 0; jj < dfs_num_k; ++jj)
 308                         {
 309                             vertex1_t j = dfs_vertices[jj];
 310                             num_edges_on_k
 311                                 -= count(adjacent_vertices(f[j], G2), f[vk]);
 312                         }
 313                     }
 314
 315                     if (num_edges_on_k != 0)
 316                         goto return_point_false;
 317                     fi_adj = adjacent_vertices(f[i], G2);
 318                     while (fi_adj.first != fi_adj.second)
 319                     {
 320                         {
 321                             vertex2_t v = *fi_adj.first;
 322                             if (invariant2(v) == invariant1(j)
 323                                 && in_S[v] == false)
 324                             {
 325                                 f[j] = v;
 326                                 in_S[v] = true;
 327                                 num_edges_on_k = 1;
 328                                 BOOST_USING_STD_MAX();
 329                                 int next_k
 330                                     = max BOOST_PREVENT_MACRO_SUBSTITUTION(
 331                                         dfs_num_k,
 332                                         max BOOST_PREVENT_MACRO_SUBSTITUTION(
 333                                             dfs_num[i], dfs_num[j]));
 334                                 match_continuation new_k;
 335                                 new_k.position
 336                                     = match_continuation::pos_fi_adj_loop;
 337                                 new_k.fi_adj = fi_adj;
 338                                 new_k.iter = iter;
 339                                 new_k.dfs_num_k = dfs_num_k;
 340                                 ++iter;
 341                                 dfs_num_k = next_k;
 342                                 k.push_back(new_k);
 343                                 goto recur;
 344                             }
 345                         }
 346                     fi_adj_loop_k:
 347                         ++fi_adj.first;
 348                     }
 349                 }
 350                 else
 351                 {
 352                     if (container_contains(adjacent_vertices(f[i], G2), f[j]))
 353                     {
 354                         ++num_edges_on_k;
 355                         match_continuation new_k;
 356                         new_k.position = match_continuation::pos_dfs_num;
 357                         k.push_back(new_k);
 358                         ++iter;
 359                         goto recur;
 360                     }
 361                 }
 362             }
 363             else
 364                 goto return_point_true;
 365             goto return_point_false;
 366
 367             {
 368             return_point_true:
 369                 return true;
 370
 371             return_point_false:
 372                 if (k.empty())
 373                     return false;
 374                 const match_continuation& this_k = k.back();
 375                 switch (this_k.position)
 376                 {
 377                 case match_continuation::pos_G2_vertex_loop:
 378                 {
 379                     G2_verts = this_k.G2_verts;
 380                     iter = this_k.iter;
 381                     dfs_num_k = this_k.dfs_num_k;
 382                     k.pop_back();
 383                     in_S[*G2_verts.first] = false;
 384                     i = source(*iter, G1);
 385                     j = target(*iter, G1);
 386                     goto G2_loop_k;
 387                 }
 388                 case match_continuation::pos_fi_adj_loop:
 389                 {
 390                     fi_adj = this_k.fi_adj;
 391                     iter = this_k.iter;
 392                     dfs_num_k = this_k.dfs_num_k;
 393                     k.pop_back();
 394                     in_S[*fi_adj.first] = false;
 395                     i = source(*iter, G1);
 396                     j = target(*iter, G1);
 397                     goto fi_adj_loop_k;
 398                 }
 399                 case match_continuation::pos_dfs_num:
 400                 {
 401                     k.pop_back();
 402                     goto return_point_false;
 403                 }
 404                 default:
 405                 {
 406                     BOOST_ASSERT(!"Bad position");
 407 #ifdef UNDER_CE
 408                     exit(-1);
 409 #else
 410                     abort();
 411 #endif
 412                 }
 413                 }
 414             }
 415         }
 416     };
 417
 418     template < typename Graph, typename InDegreeMap >
 419     void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
 420     {
 421         BGL_FORALL_VERTICES_T(v, g, Graph)
 422         put(in_degree_map, v, 0);
 423
 424         BGL_FORALL_VERTICES_T(u, g, Graph)
 425         BGL_FORALL_ADJ_T(u, v, g, Graph)
 426         put(in_degree_map, v, get(in_degree_map, v) + 1);
 427     }
 428
 429 } // namespace detail
 430
 431 template < typename InDegreeMap, typename Graph > class degree_vertex_invariant
 432 {
 433     typedef typename graph_traits< Graph >::vertex_descriptor vertex_t;
 434     typedef typename graph_traits< Graph >::degree_size_type size_type;
 435
 436 public:
 437     typedef vertex_t argument_type;
 438     typedef size_type result_type;
 439
 440     degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
 441     : m_in_degree_map(in_degree_map)
 442     , m_max_vertex_in_degree(0)
 443     , m_max_vertex_out_degree(0)
 444     , m_g(g)
 445     {
 446         BGL_FORALL_VERTICES_T(v, g, Graph)
 447         {
 448             m_max_vertex_in_degree
 449                 = (std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v));
 450             m_max_vertex_out_degree
 451                 = (std::max)(m_max_vertex_out_degree, out_degree(v, g));
 452         }
 453     }
 454
 455     size_type operator()(vertex_t v) const
 456     {
 457         return (m_max_vertex_in_degree + 1) * out_degree(v, m_g)
 458             + get(m_in_degree_map, v);
 459     }
 460     // The largest possible vertex invariant number
 461     size_type max BOOST_PREVENT_MACRO_SUBSTITUTION() const
 462     {
 463         return (m_max_vertex_in_degree + 1) * (m_max_vertex_out_degree + 1);
 464     }
 465
 466 private:
 467     InDegreeMap m_in_degree_map;
 468     size_type m_max_vertex_in_degree;
 469     size_type m_max_vertex_out_degree;
 470     const Graph& m_g;
 471 };
 472
 473 // Count actual number of vertices, even in filtered graphs.
 474 template < typename Graph > size_t count_vertices(const Graph& g)
 475 {
 476     size_t n = 0;
 477     BGL_FORALL_VERTICES_T(v, g, Graph)
 478     {
 479         (void)v;
 480         ++n;
 481     }
 482     return n;
 483 }
 484
 485 template < typename Graph1, typename Graph2, typename IsoMapping,
 486     typename Invariant1, typename Invariant2, typename IndexMap1,
 487     typename IndexMap2 >
 488 bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f,
 489     Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
 490     IndexMap1 index_map1, IndexMap2 index_map2)
 491
 492 {
 493     // Graph requirements
 494     BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph1 >));
 495     BOOST_CONCEPT_ASSERT((EdgeListGraphConcept< Graph1 >));
 496     BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph2 >));
 497     // BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph2> ));
 498
 499     typedef typename graph_traits< Graph1 >::vertex_descriptor vertex1_t;
 500     typedef typename graph_traits< Graph2 >::vertex_descriptor vertex2_t;
 501     typedef typename graph_traits< Graph1 >::vertices_size_type size_type;
 502
 503     // Vertex invariant requirement
 504     BOOST_CONCEPT_ASSERT(
 505         (AdaptableUnaryFunctionConcept< Invariant1, size_type, vertex1_t >));
 506     BOOST_CONCEPT_ASSERT(
 507         (AdaptableUnaryFunctionConcept< Invariant2, size_type, vertex2_t >));
 508
 509     // Property map requirements
 510     BOOST_CONCEPT_ASSERT(
 511         (ReadWritePropertyMapConcept< IsoMapping, vertex1_t >));
 512     typedef typename property_traits< IsoMapping >::value_type IsoMappingValue;
 513     BOOST_STATIC_ASSERT((is_convertible< IsoMappingValue, vertex2_t >::value));
 514
 515     BOOST_CONCEPT_ASSERT((ReadablePropertyMapConcept< IndexMap1, vertex1_t >));
 516     typedef typename property_traits< IndexMap1 >::value_type IndexMap1Value;
 517     BOOST_STATIC_ASSERT((is_convertible< IndexMap1Value, size_type >::value));
 518
 519     BOOST_CONCEPT_ASSERT((ReadablePropertyMapConcept< IndexMap2, vertex2_t >));
 520     typedef typename property_traits< IndexMap2 >::value_type IndexMap2Value;
 521     BOOST_STATIC_ASSERT((is_convertible< IndexMap2Value, size_type >::value));
 522
 523     if (count_vertices(G1) != count_vertices(G2))
 524         return false;
 525     if (count_vertices(G1) == 0 && count_vertices(G2) == 0)
 526         return true;
 527
 528     detail::isomorphism_algo< Graph1, Graph2, IsoMapping, Invariant1,
 529         Invariant2, IndexMap1, IndexMap2 >
 530         algo(G1, G2, f, invariant1, invariant2, max_invariant, index_map1,
 531             index_map2);
 532     return algo.test_isomorphism();
 533 }
 534
 535 namespace detail
 536 {
 537
 538     template < typename Graph1, typename Graph2, typename IsoMapping,
 539         typename IndexMap1, typename IndexMap2, typename P, typename T,
 540         typename R >
 541     bool isomorphism_impl(const Graph1& G1, const Graph2& G2, IsoMapping f,
 542         IndexMap1 index_map1, IndexMap2 index_map2,
 543         const bgl_named_params< P, T, R >& params)
 544     {
 545         std::vector< std::size_t > in_degree1_vec(num_vertices(G1));
 546         typedef safe_iterator_property_map<
 547             std::vector< std::size_t >::iterator, IndexMap1
 548 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
 549             ,
 550             std::size_t, std::size_t&
 551 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
 552             >
 553             InDeg1;
 554         InDeg1 in_degree1(
 555             in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
 556         compute_in_degree(G1, in_degree1);
 557
 558         std::vector< std::size_t > in_degree2_vec(num_vertices(G2));
 559         typedef safe_iterator_property_map<
 560             std::vector< std::size_t >::iterator, IndexMap2
 561 #ifdef BOOST_NO_STD_ITERATOR_TRAITS
 562             ,
 563             std::size_t, std::size_t&
 564 #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
 565             >
 566             InDeg2;
 567         InDeg2 in_degree2(
 568             in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
 569         compute_in_degree(G2, in_degree2);
 570
 571         degree_vertex_invariant< InDeg1, Graph1 > invariant1(in_degree1, G1);
 572         degree_vertex_invariant< InDeg2, Graph2 > invariant2(in_degree2, G2);
 573
 574         return isomorphism(G1, G2, f,
 575             choose_param(get_param(params, vertex_invariant1_t()), invariant1),
 576             choose_param(get_param(params, vertex_invariant2_t()), invariant2),
 577             choose_param(get_param(params, vertex_max_invariant_t()),
 578                 (invariant2.max)()),
 579             index_map1, index_map2);
 580     }
 581
 582     template < typename G, typename Index > struct make_degree_invariant
 583     {
 584         const G& g;
 585         const Index& index;
 586         make_degree_invariant(const G& g, const Index& index)
 587         : g(g), index(index)
 588         {
 589         }
 590         typedef typename boost::graph_traits< G >::degree_size_type
 591             degree_size_type;
 592         typedef shared_array_property_map< degree_size_type, Index >
 593             prop_map_type;
 594         typedef degree_vertex_invariant< prop_map_type, G > result_type;
 595         result_type operator()() const
 596         {
 597             prop_map_type pm = make_shared_array_property_map(
 598                 num_vertices(g), degree_size_type(), index);
 599             compute_in_degree(g, pm);
 600             return result_type(pm, g);
 601         }
 602     };
 603
 604 } // namespace detail
 605
 606 namespace graph
 607 {
 608     namespace detail
 609     {
 610         template < typename Graph1, typename Graph2 > struct isomorphism_impl
 611         {
 612             typedef bool result_type;
 613             typedef result_type type;
 614             template < typename ArgPack >
 615             bool operator()(const Graph1& g1, const Graph2& g2,
 616                 const ArgPack& arg_pack) const
 617             {
 618                 using namespace boost::graph::keywords;
 619                 typedef typename boost::detail::override_const_property_result<
 620                     ArgPack, tag::vertex_index1_map, boost::vertex_index_t,
 621                     Graph1 >::type index1_map_type;
 622                 typedef typename boost::detail::override_const_property_result<
 623                     ArgPack, tag::vertex_index2_map, boost::vertex_index_t,
 624                     Graph2 >::type index2_map_type;
 625                 index1_map_type index1_map
 626                     = boost::detail::override_const_property(
 627                         arg_pack, _vertex_index1_map, g1, boost::vertex_index);
 628                 index2_map_type index2_map
 629                     = boost::detail::override_const_property(
 630                         arg_pack, _vertex_index2_map, g2, boost::vertex_index);
 631                 typedef typename graph_traits< Graph2 >::vertex_descriptor
 632                     vertex2_t;
 633                 typename std::vector< vertex2_t >::size_type n
 634                     = (typename std::vector< vertex2_t >::size_type)
 635                         num_vertices(g1);
 636                 std::vector< vertex2_t > f(n);
 637                 typename boost::parameter::lazy_binding< ArgPack,
 638                     tag::vertex_invariant1,
 639                     boost::detail::make_degree_invariant< Graph1,
 640                         index1_map_type > >::type invariant1
 641                     = arg_pack[_vertex_invariant1
 642                         || boost::detail::make_degree_invariant< Graph1,
 643                             index1_map_type >(g1, index1_map)];
 644                 typename boost::parameter::lazy_binding< ArgPack,
 645                     tag::vertex_invariant2,
 646                     boost::detail::make_degree_invariant< Graph2,
 647                         index2_map_type > >::type invariant2
 648                     = arg_pack[_vertex_invariant2
 649                         || boost::detail::make_degree_invariant< Graph2,
 650                             index2_map_type >(g2, index2_map)];
 651                 return boost::isomorphism(g1, g2,
 652                     choose_param(
 653                         arg_pack[_isomorphism_map | boost::param_not_found()],
 654                         make_shared_array_property_map(
 655                             num_vertices(g1), vertex2_t(), index1_map)),
 656                     invariant1, invariant2,
 657                     arg_pack[_vertex_max_invariant | (invariant2.max)()],
 658                     index1_map, index2_map);
 659             }
 660         };
 661     }
 662     BOOST_GRAPH_MAKE_FORWARDING_FUNCTION(isomorphism, 2, 6)
 663 }
 664
 665 // Named parameter interface
 666 BOOST_GRAPH_MAKE_OLD_STYLE_PARAMETER_FUNCTION(isomorphism, 2)
 667
 668 // Verify that the given mapping iso_map from the vertices of g1 to the
 669 // vertices of g2 describes an isomorphism.
 670 // Note: this could be made much faster by specializing based on the graph
 671 // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
 672 // O(n^4) won't hurt us.
 673 template < typename Graph1, typename Graph2, typename IsoMap >
 674 inline bool verify_isomorphism(
 675     const Graph1& g1, const Graph2& g2, IsoMap iso_map)
 676 {
 677 #if 0
 678     // problematic for filtered_graph!
 679     if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
 680       return false;
 681 #endif
 682
 683     BGL_FORALL_EDGES_T(e1, g1, Graph1)
 684     {
 685         bool found_edge = false;
 686         BGL_FORALL_EDGES_T(e2, g2, Graph2)
 687         {
 688             if (source(e2, g2) == get(iso_map, source(e1, g1))
 689                 && target(e2, g2) == get(iso_map, target(e1, g1)))
 690             {
 691                 found_edge = true;
 692             }
 693         }
 694
 695         if (!found_edge)
 696             return false;
 697     }
 698
 699     return true;
 700 }
 701
 702 } // namespace boost
 703
 704 #ifdef BOOST_ISO_INCLUDED_ITER_MACROS
 705 #undef BOOST_ISO_INCLUDED_ITER_MACROS
 706 #include <boost/graph/iteration_macros_undef.hpp>
 707 #endif
 708
 709 #endif // BOOST_GRAPH_ISOMORPHISM_HPP