static typename edge_capacity_value<Graph, P, T, R>::type
apply
(Graph& g,
typename graph_traits<Graph>::vertex_descriptor src,
typename graph_traits<Graph>::vertex_descriptor sink,
PredMap pred,
const bgl_named_params<P, T, R>& params,
detail::error_property_not_found)
{
typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
typedef typename graph_traits<Graph>::vertices_size_type size_type;
size_type n = is_default_param(get_param(params, vertex_color)) ?
num_vertices(g) : 1;
std::vector<default_color_type> color_vec(n);
return edmunds_karp_max_flow
(g, src, sink,
choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
choose_pmap(get_param(params, edge_residual_capacity),
g, edge_residual_capacity),
choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
make_iterator_property_map(color_vec.begin(), choose_const_pmap
(get_param(params, vertex_index),
g, vertex_index), color_vec[0]),
pred);
}
typename property_traits<
typename property_map<Graph, edge_capacity_t>::const_type
>::value_type
edmunds_karp_max_flow
(Graph& g,
typename graph_traits<Graph>::vertex_descriptor src,
typename graph_traits<Graph>::vertex_descriptor sink)
{
bgl_named_params<int, buffer_param_t> params(0);
return edmunds_karp_max_flow(g, src, sink, params);
}
static typename edge_capacity_value<Graph, P, T, R>::type
apply
(Graph& g,
typename graph_traits<Graph>::vertex_descriptor src,
typename graph_traits<Graph>::vertex_descriptor sink,
PredMap pred,
const bgl_named_params<P, T, R>& params,
ColorMap color)
{
return edmunds_karp_max_flow
(g, src, sink,
choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
choose_pmap(get_param(params, edge_residual_capacity),
g, edge_residual_capacity),
choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
color, pred);
}
typename graph_traits<VertexListGraph>::degree_size_type
edge_connectivity(VertexListGraph& g, OutputIterator disconnecting_set)
{
//-------------------------------------------------------------------------
// Type Definitions
typedef graph_traits<VertexListGraph> Traits;
typedef typename Traits::vertex_iterator vertex_iterator;
typedef typename Traits::edge_iterator edge_iterator;
typedef typename Traits::out_edge_iterator out_edge_iterator;
typedef typename Traits::vertex_descriptor vertex_descriptor;
typedef typename Traits::degree_size_type degree_size_type;
typedef color_traits<default_color_type> Color;
typedef adjacency_list_traits<vecS, vecS, directedS> Tr;
typedef typename Tr::edge_descriptor Tr_edge_desc;
typedef adjacency_list<vecS, vecS, directedS, no_property,
property<edge_capacity_t, degree_size_type,
property<edge_residual_capacity_t, degree_size_type,
property<edge_reverse_t, Tr_edge_desc> > > >
FlowGraph;
typedef typename graph_traits<FlowGraph>::edge_descriptor edge_descriptor;
//-------------------------------------------------------------------------
// Variable Declarations
vertex_descriptor u, v, p, k;
edge_descriptor e1, e2;
bool inserted;
vertex_iterator vi, vi_end;
edge_iterator ei, ei_end;
degree_size_type delta, alpha_star, alpha_S_k;
std::set<vertex_descriptor> S, neighbor_S;
std::vector<vertex_descriptor> S_star, non_neighbor_S;
std::vector<default_color_type> color(num_vertices(g));
std::vector<edge_descriptor> pred(num_vertices(g));
//-------------------------------------------------------------------------
// Create a network flow graph out of the undirected graph
FlowGraph flow_g(num_vertices(g));
typename property_map<FlowGraph, edge_capacity_t>::type
cap = get(edge_capacity, flow_g);
typename property_map<FlowGraph, edge_residual_capacity_t>::type
res_cap = get(edge_residual_capacity, flow_g);
typename property_map<FlowGraph, edge_reverse_t>::type
rev_edge = get(edge_reverse, flow_g);
for (tie(ei, ei_end) = edges(g); ei != ei_end; ++ei) {
u = source(*ei, g), v = target(*ei, g);
tie(e1, inserted) = add_edge(u, v, flow_g);
cap[e1] = 1;
tie(e2, inserted) = add_edge(v, u, flow_g);
cap[e2] = 1; // not sure about this
rev_edge[e1] = e2;
rev_edge[e2] = e1;
}
//-------------------------------------------------------------------------
// The Algorithm
tie(p, delta) = detail::min_degree_vertex(g);
S_star.push_back(p);
alpha_star = delta;
S.insert(p);
neighbor_S.insert(p);
detail::neighbors(g, S.begin(), S.end(),
std::inserter(neighbor_S, neighbor_S.begin()));
std::set_difference(vertices(g).first, vertices(g).second,
neighbor_S.begin(), neighbor_S.end(),
std::back_inserter(non_neighbor_S));
while (!non_neighbor_S.empty()) { // at most n - 1 times
k = non_neighbor_S.front();
alpha_S_k = edmunds_karp_max_flow
(flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]);
if (alpha_S_k < alpha_star) {
alpha_star = alpha_S_k;
S_star.clear();
for (tie(vi, vi_end) = vertices(flow_g); vi != vi_end; ++vi)
if (color[*vi] != Color::white())
S_star.push_back(*vi);
}
S.insert(k);
neighbor_S.insert(k);
detail::neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));
non_neighbor_S.clear();
std::set_difference(vertices(g).first, vertices(g).second,
neighbor_S.begin(), neighbor_S.end(),
std::back_inserter(non_neighbor_S));
}
//-------------------------------------------------------------------------
// Compute edges of the cut [S*, ~S*]
std::vector<bool> in_S_star(num_vertices(g), false);
typename std::vector<vertex_descriptor>::iterator si;
for (si = S_star.begin(); si != S_star.end(); ++si)
in_S_star[*si] = true;
degree_size_type c = 0;
for (si = S_star.begin(); si != S_star.end(); ++si) {
out_edge_iterator ei, ei_end;
for (tie(ei, ei_end) = out_edges(*si, g); ei != ei_end; ++ei)
if (!in_S_star[target(*ei, g)]) {
*disconnecting_set++ = *ei;
++c;
}
}
return c;
}
