Edit: /usr/include/boost/graph/is_kuratowski_subgraph.hpp (10260B)
//=======================================================================
// 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__