296 lines
10 KiB
C++
296 lines
10 KiB
C++
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//=======================================================================
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// Copyright 2007 Aaron Windsor
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//=======================================================================
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#ifndef __IS_KURATOWSKI_SUBGRAPH_HPP__
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#define __IS_KURATOWSKI_SUBGRAPH_HPP__
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#include <boost/config.hpp>
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#include <boost/tuple/tuple.hpp> //for tie
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#include <boost/property_map/property_map.hpp>
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#include <boost/graph/properties.hpp>
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#include <boost/graph/isomorphism.hpp>
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#include <boost/graph/adjacency_list.hpp>
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#include <algorithm>
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#include <vector>
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#include <set>
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namespace boost
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{
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namespace detail
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{
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template < typename Graph > Graph make_K_5()
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{
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typename graph_traits< Graph >::vertex_iterator vi, vi_end, inner_vi;
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Graph K_5(5);
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for (boost::tie(vi, vi_end) = vertices(K_5); vi != vi_end; ++vi)
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for (inner_vi = next(vi); inner_vi != vi_end; ++inner_vi)
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add_edge(*vi, *inner_vi, K_5);
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return K_5;
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}
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template < typename Graph > Graph make_K_3_3()
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{
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typename graph_traits< Graph >::vertex_iterator vi, vi_end,
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bipartition_start, inner_vi;
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Graph K_3_3(6);
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bipartition_start = next(next(next(vertices(K_3_3).first)));
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for (boost::tie(vi, vi_end) = vertices(K_3_3); vi != bipartition_start;
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++vi)
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for (inner_vi = bipartition_start; inner_vi != vi_end; ++inner_vi)
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add_edge(*vi, *inner_vi, K_3_3);
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return K_3_3;
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}
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template < typename AdjacencyList, typename Vertex >
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void contract_edge(AdjacencyList& neighbors, Vertex u, Vertex v)
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{
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// Remove u from v's neighbor list
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neighbors[v].erase(
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std::remove(neighbors[v].begin(), neighbors[v].end(), u),
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neighbors[v].end());
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// Replace any references to u with references to v
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typedef
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typename AdjacencyList::value_type::iterator adjacency_iterator_t;
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adjacency_iterator_t u_neighbor_end = neighbors[u].end();
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for (adjacency_iterator_t u_neighbor_itr = neighbors[u].begin();
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u_neighbor_itr != u_neighbor_end; ++u_neighbor_itr)
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{
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Vertex u_neighbor(*u_neighbor_itr);
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std::replace(neighbors[u_neighbor].begin(),
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neighbors[u_neighbor].end(), u, v);
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}
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// Remove v from u's neighbor list
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neighbors[u].erase(
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std::remove(neighbors[u].begin(), neighbors[u].end(), v),
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neighbors[u].end());
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// Add everything in u's neighbor list to v's neighbor list
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std::copy(neighbors[u].begin(), neighbors[u].end(),
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std::back_inserter(neighbors[v]));
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// Clear u's neighbor list
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neighbors[u].clear();
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}
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enum target_graph_t
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{
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tg_k_3_3,
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tg_k_5
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};
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} // namespace detail
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template < typename Graph, typename ForwardIterator, typename VertexIndexMap >
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bool is_kuratowski_subgraph(const Graph& g, ForwardIterator begin,
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ForwardIterator end, VertexIndexMap vm)
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{
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typedef typename graph_traits< Graph >::vertex_descriptor vertex_t;
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typedef typename graph_traits< Graph >::vertex_iterator vertex_iterator_t;
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typedef typename graph_traits< Graph >::edge_descriptor edge_t;
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typedef typename graph_traits< Graph >::edges_size_type e_size_t;
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typedef typename graph_traits< Graph >::vertices_size_type v_size_t;
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typedef typename std::vector< vertex_t > v_list_t;
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typedef typename v_list_t::iterator v_list_iterator_t;
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typedef iterator_property_map< typename std::vector< v_list_t >::iterator,
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VertexIndexMap >
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vertex_to_v_list_map_t;
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typedef adjacency_list< vecS, vecS, undirectedS > small_graph_t;
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detail::target_graph_t target_graph
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= detail::tg_k_3_3; // unless we decide otherwise later
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static small_graph_t K_5(detail::make_K_5< small_graph_t >());
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static small_graph_t K_3_3(detail::make_K_3_3< small_graph_t >());
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v_size_t n_vertices(num_vertices(g));
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v_size_t max_num_edges(3 * n_vertices - 5);
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std::vector< v_list_t > neighbors_vector(n_vertices);
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vertex_to_v_list_map_t neighbors(neighbors_vector.begin(), vm);
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e_size_t count = 0;
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for (ForwardIterator itr = begin; itr != end; ++itr)
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{
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if (count++ > max_num_edges)
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return false;
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edge_t e(*itr);
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vertex_t u(source(e, g));
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vertex_t v(target(e, g));
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neighbors[u].push_back(v);
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neighbors[v].push_back(u);
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}
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for (v_size_t max_size = 2; max_size < 5; ++max_size)
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{
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vertex_iterator_t vi, vi_end;
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for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
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{
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vertex_t v(*vi);
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// a hack to make sure we don't contract the middle edge of a path
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// of four degree-3 vertices
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if (max_size == 4 && neighbors[v].size() == 3)
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{
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if (neighbors[neighbors[v][0]].size()
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+ neighbors[neighbors[v][1]].size()
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+ neighbors[neighbors[v][2]].size()
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< 11 // so, it has two degree-3 neighbors
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)
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continue;
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}
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while (neighbors[v].size() > 0 && neighbors[v].size() < max_size)
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{
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// Find one of v's neighbors u such that v and u
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// have no neighbors in common. We'll look for such a
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// neighbor with a naive cubic-time algorithm since the
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// max size of any of the neighbor sets we'll consider
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// merging is 3
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bool neighbor_sets_intersect = false;
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vertex_t min_u = graph_traits< Graph >::null_vertex();
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vertex_t u;
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v_list_iterator_t v_neighbor_end = neighbors[v].end();
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for (v_list_iterator_t v_neighbor_itr = neighbors[v].begin();
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v_neighbor_itr != v_neighbor_end; ++v_neighbor_itr)
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{
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neighbor_sets_intersect = false;
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u = *v_neighbor_itr;
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v_list_iterator_t u_neighbor_end = neighbors[u].end();
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for (v_list_iterator_t u_neighbor_itr
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= neighbors[u].begin();
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u_neighbor_itr != u_neighbor_end
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&& !neighbor_sets_intersect;
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++u_neighbor_itr)
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{
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for (v_list_iterator_t inner_v_neighbor_itr
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= neighbors[v].begin();
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inner_v_neighbor_itr != v_neighbor_end;
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++inner_v_neighbor_itr)
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{
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if (*u_neighbor_itr == *inner_v_neighbor_itr)
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{
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neighbor_sets_intersect = true;
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break;
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}
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}
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}
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if (!neighbor_sets_intersect
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&& (min_u == graph_traits< Graph >::null_vertex()
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|| neighbors[u].size() < neighbors[min_u].size()))
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{
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min_u = u;
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}
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}
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if (min_u == graph_traits< Graph >::null_vertex())
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// Exited the loop without finding an appropriate neighbor
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// of v, so v must be a lost cause. Move on to other
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// vertices.
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break;
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else
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u = min_u;
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detail::contract_edge(neighbors, u, v);
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} // end iteration over v's neighbors
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} // end iteration through vertices v
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if (max_size == 3)
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{
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// check to see whether we should go on to find a K_5
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for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
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if (neighbors[*vi].size() == 4)
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{
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target_graph = detail::tg_k_5;
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break;
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}
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if (target_graph == detail::tg_k_3_3)
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break;
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}
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} // end iteration through max degree 2,3, and 4
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// Now, there should only be 5 or 6 vertices with any neighbors. Find them.
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v_list_t main_vertices;
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vertex_iterator_t vi, vi_end;
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for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
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{
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if (!neighbors[*vi].empty())
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main_vertices.push_back(*vi);
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}
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// create a graph isomorphic to the contracted graph to test
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// against K_5 and K_3_3
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small_graph_t contracted_graph(main_vertices.size());
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std::map< vertex_t,
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typename graph_traits< small_graph_t >::vertex_descriptor >
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contracted_vertex_map;
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typename v_list_t::iterator itr, itr_end;
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itr_end = main_vertices.end();
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typename graph_traits< small_graph_t >::vertex_iterator si
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= vertices(contracted_graph).first;
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for (itr = main_vertices.begin(); itr != itr_end; ++itr, ++si)
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{
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contracted_vertex_map[*itr] = *si;
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}
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typename v_list_t::iterator jtr, jtr_end;
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for (itr = main_vertices.begin(); itr != itr_end; ++itr)
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{
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jtr_end = neighbors[*itr].end();
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for (jtr = neighbors[*itr].begin(); jtr != jtr_end; ++jtr)
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{
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if (get(vm, *itr) < get(vm, *jtr))
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{
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add_edge(contracted_vertex_map[*itr],
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contracted_vertex_map[*jtr], contracted_graph);
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}
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}
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}
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if (target_graph == detail::tg_k_5)
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{
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return boost::isomorphism(K_5, contracted_graph);
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}
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else // target_graph == tg_k_3_3
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{
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return boost::isomorphism(K_3_3, contracted_graph);
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}
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}
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template < typename Graph, typename ForwardIterator >
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bool is_kuratowski_subgraph(
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const Graph& g, ForwardIterator begin, ForwardIterator end)
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{
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return is_kuratowski_subgraph(g, begin, end, get(vertex_index, g));
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}
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}
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#endif //__IS_KURATOWSKI_SUBGRAPH_HPP__
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