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//======================================================================= // 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 #include //for tie #include #include #include #include #include #include #include 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 (boost::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 (boost::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 (boost::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 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 (boost::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 (boost::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 boost::isomorphism(K_5, contracted_graph); } else // target_graph == tg_k_3_3 { return boost::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__