#define __IS_KURATOWSKI_SUBGRAPH_HPP__
#include <boost/config.hpp>
-#include <boost/tuple/tuple.hpp> //for tie
+#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 <vector>
#include <set>
-
-
namespace boost
{
-
- namespace detail
- {
- template <typename Graph>
- Graph make_K_5()
+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;
+ 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()
+ 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;
+ 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>
+ 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
- )
+ // 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
- );
+ 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};
+ // Remove v from u's neighbor list
+ neighbors[u].erase(
+ std::remove(neighbors[u].begin(), neighbors[u].end(), v),
+ neighbors[u].end());
- } // namespace detail
+ // 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
- )
- {
+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 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 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;
+ 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
+ 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_5(detail::make_K_5< small_graph_t >());
- static small_graph_t K_3_3(detail::make_K_3_3<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);
+ v_size_t max_num_edges(3 * n_vertices - 5);
- std::vector<v_list_t> neighbors_vector(n_vertices);
+ 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)
- {
+ for (ForwardIterator itr = begin; itr != end; ++itr)
+ {
if (count++ > max_num_edges)
- return false;
+ return false;
edge_t e(*itr);
- vertex_t u(source(e,g));
- vertex_t v(target(e,g));
+ 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)
- {
+ 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)
- {
+ 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
+ // 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()
+ {
+ 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;
- }
+ )
+ 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
+ // 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 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
- )
- {
+ 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
- )
- {
+ 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())
- )
- {
+ }
+ }
+ }
+ 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;
+ }
+ }
+
+ 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;
+ u = min_u;
detail::contract_edge(neighbors, u, v);
- }//end iteration over v's neighbors
+ } // end iteration over v's neighbors
- }//end iteration through vertices v
+ } // 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)
+ for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
+ if (neighbors[*vi].size() == 4)
{
- target_graph = detail::tg_k_5;
- break;
+ 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.
-
+ 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)
- {
+
+ 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
+ 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;
-
+ 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)
- {
+ 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)
- {
+ 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))
- {
+ 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));
- }
+ 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__
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