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boost/graph/is_kuratowski_subgraph.hpp

//=======================================================================
// Copyright 2007 Aaron Windsor
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================
#ifndef __IS_KURATOWSKI_SUBGRAPH_HPP__
#define __IS_KURATOWSKI_SUBGRAPH_HPP__

#include <boost/config.hpp>
#include <boost/utility.hpp> //for next/prior
#include <boost/tuple/tuple.hpp>   //for tie
#include <boost/property_map/property_map.hpp>
#include <boost/graph/properties.hpp>
#include <boost/graph/isomorphism.hpp>
#include <boost/graph/adjacency_list.hpp>

#include <algorithm>
#include <vector>
#include <set>



namespace boost
{
  
  namespace detail
  {

    template <typename Graph>
    Graph make_K_5()
    {
      typename graph_traits<Graph>::vertex_iterator vi, vi_end, inner_vi;
      Graph K_5(5);
      for(tie(vi,vi_end) = vertices(K_5); vi != vi_end; ++vi)
        for(inner_vi = next(vi); inner_vi != vi_end; ++inner_vi)
          add_edge(*vi, *inner_vi, K_5);
      return K_5;
    }


    template <typename Graph>
    Graph make_K_3_3()
    {
      typename graph_traits<Graph>::vertex_iterator 
        vi, vi_end, bipartition_start, inner_vi;
      Graph K_3_3(6);
      bipartition_start = next(next(next(vertices(K_3_3).first)));
      for(tie(vi, vi_end) = vertices(K_3_3); vi != bipartition_start; ++vi)
        for(inner_vi= bipartition_start; inner_vi != vi_end; ++inner_vi)
          add_edge(*vi, *inner_vi, K_3_3);
      return K_3_3;
    }


    template <typename AdjacencyList, typename Vertex>
    void contract_edge(AdjacencyList& neighbors, Vertex u, Vertex v)
    {
      // Remove u from v's neighbor list
      neighbors[v].erase(std::remove(neighbors[v].begin(), 
                                     neighbors[v].end(), u
                                     ), 
                         neighbors[v].end()
                         );
      
      // Replace any references to u with references to v
      typedef typename AdjacencyList::value_type::iterator 
        adjacency_iterator_t;
      
      adjacency_iterator_t u_neighbor_end = neighbors[u].end();
      for(adjacency_iterator_t u_neighbor_itr = neighbors[u].begin();
          u_neighbor_itr != u_neighbor_end; ++u_neighbor_itr
          )
        {
          Vertex u_neighbor(*u_neighbor_itr);
          std::replace(neighbors[u_neighbor].begin(), 
                       neighbors[u_neighbor].end(), u, v
                       );
        }
      
      // Remove v from u's neighbor list
      neighbors[u].erase(std::remove(neighbors[u].begin(), 
                                     neighbors[u].end(), v
                                     ), 
                         neighbors[u].end()
                         );
      
      // Add everything in u's neighbor list to v's neighbor list
      std::copy(neighbors[u].begin(), 
                neighbors[u].end(), 
                std::back_inserter(neighbors[v])
                );
      
      // Clear u's neighbor list
      neighbors[u].clear();

    }

    enum target_graph_t { tg_k_3_3, tg_k_5};

  } // namespace detail




  template <typename Graph, typename ForwardIterator, typename VertexIndexMap>
  bool is_kuratowski_subgraph(const Graph& g,
                              ForwardIterator begin, 
                              ForwardIterator end, 
                              VertexIndexMap vm
                              )
  {

    typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
    typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
    typedef typename graph_traits<Graph>::edge_descriptor edge_t;
    typedef typename graph_traits<Graph>::edges_size_type e_size_t;
    typedef typename graph_traits<Graph>::vertices_size_type v_size_t;
    typedef typename std::vector<vertex_t> v_list_t;
    typedef typename v_list_t::iterator v_list_iterator_t;
    typedef iterator_property_map
      <typename std::vector<v_list_t>::iterator, VertexIndexMap> 
      vertex_to_v_list_map_t;

    typedef adjacency_list<vecS, vecS, undirectedS> small_graph_t;

    detail::target_graph_t target_graph = detail::tg_k_3_3; //unless we decide otherwise later

    static small_graph_t K_5(detail::make_K_5<small_graph_t>());

    static small_graph_t K_3_3(detail::make_K_3_3<small_graph_t>());

    v_size_t n_vertices(num_vertices(g));
    v_size_t max_num_edges(3*n_vertices - 5);

    std::vector<v_list_t> neighbors_vector(n_vertices);
    vertex_to_v_list_map_t neighbors(neighbors_vector.begin(), vm);

    e_size_t count = 0;
    for(ForwardIterator itr = begin; itr != end; ++itr)
      {

        if (count++ > max_num_edges)
          return false;

        edge_t e(*itr);
        vertex_t u(source(e,g));
        vertex_t v(target(e,g));

        neighbors[u].push_back(v);
        neighbors[v].push_back(u);

      }


    for(v_size_t max_size = 2; max_size < 5; ++max_size)
      {

        vertex_iterator_t vi, vi_end;
        for(tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
          {
            vertex_t v(*vi);

            //a hack to make sure we don't contract the middle edge of a path
            //of four degree-3 vertices
            if (max_size == 4 && neighbors[v].size() == 3)
              {
                if (neighbors[neighbors[v][0]].size() +
                    neighbors[neighbors[v][1]].size() +
                    neighbors[neighbors[v][2]].size()
                    < 11 // so, it has two degree-3 neighbors
                    )
                  continue;
              }

            while (neighbors[v].size() > 0 && neighbors[v].size() < max_size)
              {
                // Find one of v's neighbors u such that that v and u
                // have no neighbors in common. We'll look for such a 
                // neighbor with a naive cubic-time algorithm since the 
                // max size of any of the neighbor sets we'll consider 
                // merging is 3
                
                bool neighbor_sets_intersect = false;
                
                vertex_t min_u = graph_traits<Graph>::null_vertex();
                vertex_t u;
                v_list_iterator_t v_neighbor_end = neighbors[v].end();
                for(v_list_iterator_t v_neighbor_itr = neighbors[v].begin();
                    v_neighbor_itr != v_neighbor_end; 
                    ++v_neighbor_itr
                    )
                  {
                    neighbor_sets_intersect = false;
                    u = *v_neighbor_itr;
                    v_list_iterator_t u_neighbor_end = neighbors[u].end();
                    for(v_list_iterator_t u_neighbor_itr = 
                          neighbors[u].begin();
                        u_neighbor_itr != u_neighbor_end && 
                          !neighbor_sets_intersect; 
                        ++u_neighbor_itr
                        )
                      {
                        for(v_list_iterator_t inner_v_neighbor_itr = 
                              neighbors[v].begin();
                            inner_v_neighbor_itr != v_neighbor_end; 
                            ++inner_v_neighbor_itr
                            )
                          {
                            if (*u_neighbor_itr == *inner_v_neighbor_itr)
                              {
                                neighbor_sets_intersect = true;
                                break;
                              }
                          }
                        
                      }
                    if (!neighbor_sets_intersect &&
                        (min_u == graph_traits<Graph>::null_vertex() || 
                         neighbors[u].size() < neighbors[min_u].size())
                        )
                      {
                        min_u = u;
                      }
                        
                  }

                if (min_u == graph_traits<Graph>::null_vertex())
                  // Exited the loop without finding an appropriate neighbor of
                  // v, so v must be a lost cause. Move on to other vertices.
                  break;
                else
                  u = min_u;

                detail::contract_edge(neighbors, u, v);

              }//end iteration over v's neighbors

          }//end iteration through vertices v

        if (max_size == 3)
          {
            // check to see whether we should go on to find a K_5
            for(tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
              if (neighbors[*vi].size() == 4)
                {
                  target_graph = detail::tg_k_5;
                  break;
                }

            if (target_graph == detail::tg_k_3_3)
              break;
          }
        
      }//end iteration through max degree 2,3, and 4

    
    //Now, there should only be 5 or 6 vertices with any neighbors. Find them.
    
    v_list_t main_vertices;
    vertex_iterator_t vi, vi_end;
    
    for(tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
      {
        if (!neighbors[*vi].empty())
          main_vertices.push_back(*vi);
      }
    
    // create a graph isomorphic to the contracted graph to test 
    // against K_5 and K_3_3
    small_graph_t contracted_graph(main_vertices.size());
    std::map<vertex_t,typename graph_traits<small_graph_t>::vertex_descriptor> 
      contracted_vertex_map;
    
    typename v_list_t::iterator itr, itr_end;
    itr_end = main_vertices.end();
    typename graph_traits<small_graph_t>::vertex_iterator 
      si = vertices(contracted_graph).first;
    
    for(itr = main_vertices.begin(); itr != itr_end; ++itr, ++si)
      {
        contracted_vertex_map[*itr] = *si;
      }

    typename v_list_t::iterator jtr, jtr_end;
    for(itr = main_vertices.begin(); itr != itr_end; ++itr)
      {
        jtr_end = neighbors[*itr].end();
        for(jtr = neighbors[*itr].begin(); jtr != jtr_end; ++jtr)
          {
            if (get(vm,*itr) < get(vm,*jtr))
              {
                add_edge(contracted_vertex_map[*itr],
                         contracted_vertex_map[*jtr],
                         contracted_graph
                         );
              }
          }
      }
    
    if (target_graph == detail::tg_k_5)
      {
        return isomorphism(K_5,contracted_graph);
      }
    else //target_graph == tg_k_3_3
      {
        return isomorphism(K_3_3,contracted_graph);
      }
    
    
  }





  template <typename Graph, typename ForwardIterator>
  bool is_kuratowski_subgraph(const Graph& g, 
                              ForwardIterator begin, 
                              ForwardIterator end
                              )
  {
    return is_kuratowski_subgraph(g, begin, end, get(vertex_index,g));
  }



  
}

#endif //__IS_KURATOWSKI_SUBGRAPH_HPP__