/** add a new vertex into the kernel
* \return the handle of the vertex
*/
VertexHandle TopologyKernel::new_vertex()
{
vertices_.push_back(Vertex());
v_properties_resize(n_vertices());
return handle(vertices_.back());
}
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 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);
}
}