isomorphism.hpp

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// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
//
// Permission to copy, use, sell and distribute this software is granted
// provided this copyright notice appears in all copies.
// Permission to modify the code and to distribute modified code is granted
// provided this copyright notice appears in all copies, and a notice
// that the code was modified is included with the copyright notice.
//
// This software is provided "as is" without express or implied warranty,
// and with no claim as to its suitability for any purpose.
#ifndef BOOST_GRAPH_ISOMORPHISM_HPP
#define BOOST_GRAPH_ISOMORPHISM_HPP

#include <utility>
#include <vector>
#include <iterator>
#include <algorithm>
#include <boost/config.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/utility.hpp>
#include <boost/detail/algorithm.hpp>
#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap

#ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
#define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
#include <boost/graph/iteration_macros.hpp>
#endif

namespace boost {

  namespace detail {

    template <typename Graph1, typename Graph2, typename IsoMapping,
      typename Invariant1, typename Invariant2,
      typename IndexMap1, typename IndexMap2>
    class isomorphism_algo
    {
      typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
      typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
      typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
      typedef typename graph_traits<Graph1>::vertices_size_type size_type;
      typedef typename Invariant1::result_type invar1_value;
      typedef typename Invariant2::result_type invar2_value;
    
      const Graph1& G1;
      const Graph2& G2;
      IsoMapping f;
      Invariant1 invariant1;
      Invariant2 invariant2;
      std::size_t max_invariant;
      IndexMap1 index_map1;
      IndexMap2 index_map2;
    
      std::vector<vertex1_t> dfs_vertices;
      typedef typename std::vector<vertex1_t>::iterator vertex_iter;
      std::vector<int> dfs_num_vec;
      typedef safe_iterator_property_map<typename std::vector<int>::iterator,
                                         IndexMap1
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
                                         , int, int&
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
                                         > DFSNumMap;
      DFSNumMap dfs_num;
      std::vector<edge1_t> ordered_edges;
      typedef typename std::vector<edge1_t>::iterator edge_iter;
    
      std::vector<char> in_S_vec;
      typedef safe_iterator_property_map<typename std::vector<char>::iterator,
                                         IndexMap2
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
                                         , char, char&
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
                                         > InSMap;
      InSMap in_S;
    
      int num_edges_on_k;
    
      friend struct compare_multiplicity;
      struct compare_multiplicity
      {
        compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
          : invariant1(invariant1), multiplicity(multiplicity) { }
        bool operator()(const vertex1_t& x, const vertex1_t& y) const {
          return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
        }
        Invariant1 invariant1;
        size_type* multiplicity;
      };
    
      struct record_dfs_order : default_dfs_visitor
      {
        record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 
          : vertices(v), edges(e) { }
    
        void discover_vertex(vertex1_t v, const Graph1&) const {
          vertices.push_back(v);
        }
        void examine_edge(edge1_t e, const Graph1& G1) const {
          edges.push_back(e);
        }
        std::vector<vertex1_t>& vertices;
        std::vector<edge1_t>& edges;
      };
    
      struct edge_cmp {
        edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
          : G1(G1), dfs_num(dfs_num) { }
        bool operator()(const edge1_t& e1, const edge1_t& e2) const {
          using namespace std;
          int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
          int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
          int m1 = (max)(u1, v1);
          int m2 = (max)(u2, v2);
          // lexicographical comparison 
          return std::make_pair(m1, std::make_pair(u1, v1))
            < std::make_pair(m2, std::make_pair(u2, v2));
        }
        const Graph1& G1;
        DFSNumMap dfs_num;
      };
    
    public:
      isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
                       Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
                       IndexMap1 index_map1, IndexMap2 index_map2)
        : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
          max_invariant(max_invariant),
          index_map1(index_map1), index_map2(index_map2)
      {
        in_S_vec.resize(num_vertices(G1));
        in_S = make_safe_iterator_property_map
          (in_S_vec.begin(), in_S_vec.size(), index_map2
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
           , in_S_vec.front()
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
           );
      }
    
      bool test_isomorphism()
      {
        {
          std::vector<invar1_value> invar1_array;
          BGL_FORALL_VERTICES_T(v, G1, Graph1)
            invar1_array.push_back(invariant1(v));
          sort(invar1_array);
        
          std::vector<invar2_value> invar2_array;
          BGL_FORALL_VERTICES_T(v, G2, Graph2)
            invar2_array.push_back(invariant2(v));
          sort(invar2_array);
          if (! equal(invar1_array, invar2_array))
            return false;
        }
        
        std::vector<vertex1_t> V_mult;
        BGL_FORALL_VERTICES_T(v, G1, Graph1)
          V_mult.push_back(v);
        {
          std::vector<size_type> multiplicity(max_invariant, 0);
          BGL_FORALL_VERTICES_T(v, G1, Graph1)
            ++multiplicity[invariant1(v)];
          sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
        }
        
        std::vector<default_color_type> color_vec(num_vertices(G1));
        safe_iterator_property_map<std::vector<default_color_type>::iterator,
                                   IndexMap1
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
                                   , default_color_type, default_color_type&
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
                                   >
          color_map(color_vec.begin(), color_vec.size(), index_map1);
        record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
        typedef color_traits<default_color_type> Color;
        for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
          if (color_map[*u] == Color::white()) {
            dfs_visitor.start_vertex(*u, G1);
            depth_first_visit(G1, *u, dfs_visitor, color_map);
          }
        }
        // Create the dfs_num array and dfs_num_map
        dfs_num_vec.resize(num_vertices(G1));
        dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
                                                  dfs_num_vec.size(), 
                                                  index_map1
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
                                                  , dfs_num_vec.front()
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
                                                  );
        size_type n = 0;
        for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
          dfs_num[*v] = n++;
        
        sort(ordered_edges, edge_cmp(G1, dfs_num));
        
    
        int dfs_num_k = -1;
        return this->match(ordered_edges.begin(), dfs_num_k);
      }
    
    private:
      bool match(edge_iter iter, int dfs_num_k)
      {
        if (iter != ordered_edges.end()) {
          vertex1_t i = source(*iter, G1), j = target(*iter, G2);
          if (dfs_num[i] > dfs_num_k) {
            vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
            BGL_FORALL_VERTICES_T(u, G2, Graph2) {
              if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
                f[kp1] = u;
                in_S[u] = true;
                num_edges_on_k = 0;
                
                if (match(iter, dfs_num_k + 1))
#if 0
                    // dwa 2003/7/11 -- this *HAS* to be a bug!
                    ;
#endif 
                    return true;
                    
                in_S[u] = false;
              }
            }
               
          }
          else if (dfs_num[j] > dfs_num_k) {
            vertex1_t k = dfs_vertices[dfs_num_k];
            num_edges_on_k -= 
              count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));
                
            for (int jj = 0; jj < dfs_num_k; ++jj) {
              vertex1_t j = dfs_vertices[jj];
              num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);
            }
                
            if (num_edges_on_k != 0)
              return false;