184 lines
6.7 KiB
C++
184 lines
6.7 KiB
C++
//=======================================================================
|
|
// Copyright 2000 University of Notre Dame.
|
|
// Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee
|
|
//
|
|
// 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 BOOST_EDGE_CONNECTIVITY
|
|
#define BOOST_EDGE_CONNECTIVITY
|
|
|
|
// WARNING: not-yet fully tested!
|
|
|
|
#include <boost/config.hpp>
|
|
#include <vector>
|
|
#include <set>
|
|
#include <algorithm>
|
|
#include <boost/graph/edmonds_karp_max_flow.hpp>
|
|
|
|
namespace boost {
|
|
|
|
namespace detail {
|
|
|
|
template <class Graph>
|
|
inline
|
|
std::pair<typename graph_traits<Graph>::vertex_descriptor,
|
|
typename graph_traits<Graph>::degree_size_type>
|
|
min_degree_vertex(Graph& g)
|
|
{
|
|
typedef graph_traits<Graph> Traits;
|
|
typename Traits::vertex_descriptor p;
|
|
typedef typename Traits::degree_size_type size_type;
|
|
size_type delta = (std::numeric_limits<size_type>::max)();
|
|
|
|
typename Traits::vertex_iterator i, iend;
|
|
for (boost::tie(i, iend) = vertices(g); i != iend; ++i)
|
|
if (degree(*i, g) < delta) {
|
|
delta = degree(*i, g);
|
|
p = *i;
|
|
}
|
|
return std::make_pair(p, delta);
|
|
}
|
|
|
|
template <class Graph, class OutputIterator>
|
|
void neighbors(const Graph& g,
|
|
typename graph_traits<Graph>::vertex_descriptor u,
|
|
OutputIterator result)
|
|
{
|
|
typename graph_traits<Graph>::adjacency_iterator ai, aend;
|
|
for (boost::tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)
|
|
*result++ = *ai;
|
|
}
|
|
|
|
template <class Graph, class VertexIterator, class OutputIterator>
|
|
void neighbors(const Graph& g,
|
|
VertexIterator first, VertexIterator last,
|
|
OutputIterator result)
|
|
{
|
|
for (; first != last; ++first)
|
|
neighbors(g, *first, result);
|
|
}
|
|
|
|
} // namespace detail
|
|
|
|
// O(m n)
|
|
template <class VertexListGraph, class OutputIterator>
|
|
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 (boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei) {
|
|
u = source(*ei, g), v = target(*ei, g);
|
|
boost::tie(e1, inserted) = add_edge(u, v, flow_g);
|
|
cap[e1] = 1;
|
|
boost::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
|
|
|
|
boost::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()));
|
|
|
|
boost::tie(vi, vi_end) = vertices(g);
|
|
std::set_difference(vi, vi_end,
|
|
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 = edmonds_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 (boost::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();
|
|
boost::tie(vi, vi_end) = vertices(g);
|
|
std::set_difference(vi, vi_end,
|
|
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 (boost::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;
|
|
}
|
|
|
|
} // namespace boost
|
|
|
|
#endif // BOOST_EDGE_CONNECTIVITY
|