188 lines
6.6 KiB
C++
188 lines
6.6 KiB
C++
//=======================================================================
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// Copyright 2000 University of Notre Dame.
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// Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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//=======================================================================
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#ifndef BOOST_EDGE_CONNECTIVITY
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#define BOOST_EDGE_CONNECTIVITY
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// WARNING: not-yet fully tested!
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#include <boost/config.hpp>
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#include <vector>
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#include <set>
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#include <algorithm>
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#include <boost/graph/edmonds_karp_max_flow.hpp>
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namespace boost
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{
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namespace detail
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{
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template < class Graph >
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inline std::pair< typename graph_traits< Graph >::vertex_descriptor,
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typename graph_traits< Graph >::degree_size_type >
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min_degree_vertex(Graph& g)
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{
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typedef graph_traits< Graph > Traits;
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typename Traits::vertex_descriptor p;
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typedef typename Traits::degree_size_type size_type;
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size_type delta = (std::numeric_limits< size_type >::max)();
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typename Traits::vertex_iterator i, iend;
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for (boost::tie(i, iend) = vertices(g); i != iend; ++i)
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if (degree(*i, g) < delta)
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{
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delta = degree(*i, g);
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p = *i;
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}
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return std::make_pair(p, delta);
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}
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template < class Graph, class OutputIterator >
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void neighbors(const Graph& g,
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typename graph_traits< Graph >::vertex_descriptor u,
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OutputIterator result)
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{
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typename graph_traits< Graph >::adjacency_iterator ai, aend;
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for (boost::tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)
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*result++ = *ai;
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}
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template < class Graph, class VertexIterator, class OutputIterator >
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void neighbors(const Graph& g, VertexIterator first, VertexIterator last,
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OutputIterator result)
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{
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for (; first != last; ++first)
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neighbors(g, *first, result);
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}
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} // namespace detail
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// O(m n)
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template < class VertexListGraph, class OutputIterator >
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typename graph_traits< VertexListGraph >::degree_size_type edge_connectivity(
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VertexListGraph& g, OutputIterator disconnecting_set)
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{
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//-------------------------------------------------------------------------
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// Type Definitions
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typedef graph_traits< VertexListGraph > Traits;
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typedef typename Traits::vertex_iterator vertex_iterator;
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typedef typename Traits::edge_iterator edge_iterator;
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typedef typename Traits::out_edge_iterator out_edge_iterator;
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typedef typename Traits::vertex_descriptor vertex_descriptor;
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typedef typename Traits::degree_size_type degree_size_type;
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typedef color_traits< default_color_type > Color;
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typedef adjacency_list_traits< vecS, vecS, directedS > Tr;
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typedef typename Tr::edge_descriptor Tr_edge_desc;
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typedef adjacency_list< vecS, vecS, directedS, no_property,
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property< edge_capacity_t, degree_size_type,
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property< edge_residual_capacity_t, degree_size_type,
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property< edge_reverse_t, Tr_edge_desc > > > >
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FlowGraph;
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typedef typename graph_traits< FlowGraph >::edge_descriptor edge_descriptor;
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//-------------------------------------------------------------------------
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// Variable Declarations
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vertex_descriptor u, v, p, k;
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edge_descriptor e1, e2;
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bool inserted;
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vertex_iterator vi, vi_end;
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edge_iterator ei, ei_end;
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degree_size_type delta, alpha_star, alpha_S_k;
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std::set< vertex_descriptor > S, neighbor_S;
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std::vector< vertex_descriptor > S_star, non_neighbor_S;
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std::vector< default_color_type > color(num_vertices(g));
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std::vector< edge_descriptor > pred(num_vertices(g));
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//-------------------------------------------------------------------------
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// Create a network flow graph out of the undirected graph
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FlowGraph flow_g(num_vertices(g));
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typename property_map< FlowGraph, edge_capacity_t >::type cap
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= get(edge_capacity, flow_g);
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typename property_map< FlowGraph, edge_residual_capacity_t >::type res_cap
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= get(edge_residual_capacity, flow_g);
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typename property_map< FlowGraph, edge_reverse_t >::type rev_edge
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= get(edge_reverse, flow_g);
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for (boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
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{
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u = source(*ei, g), v = target(*ei, g);
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boost::tie(e1, inserted) = add_edge(u, v, flow_g);
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cap[e1] = 1;
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boost::tie(e2, inserted) = add_edge(v, u, flow_g);
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cap[e2] = 1; // not sure about this
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rev_edge[e1] = e2;
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rev_edge[e2] = e1;
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}
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//-------------------------------------------------------------------------
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// The Algorithm
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boost::tie(p, delta) = detail::min_degree_vertex(g);
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S_star.push_back(p);
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alpha_star = delta;
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S.insert(p);
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neighbor_S.insert(p);
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detail::neighbors(
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g, S.begin(), S.end(), std::inserter(neighbor_S, neighbor_S.begin()));
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boost::tie(vi, vi_end) = vertices(g);
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std::set_difference(vi, vi_end, neighbor_S.begin(), neighbor_S.end(),
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std::back_inserter(non_neighbor_S));
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while (!non_neighbor_S.empty())
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{ // at most n - 1 times
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k = non_neighbor_S.front();
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alpha_S_k = edmonds_karp_max_flow(
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flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]);
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if (alpha_S_k < alpha_star)
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{
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alpha_star = alpha_S_k;
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S_star.clear();
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for (boost::tie(vi, vi_end) = vertices(flow_g); vi != vi_end; ++vi)
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if (color[*vi] != Color::white())
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S_star.push_back(*vi);
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}
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S.insert(k);
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neighbor_S.insert(k);
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detail::neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));
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non_neighbor_S.clear();
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boost::tie(vi, vi_end) = vertices(g);
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std::set_difference(vi, vi_end, neighbor_S.begin(), neighbor_S.end(),
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std::back_inserter(non_neighbor_S));
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}
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//-------------------------------------------------------------------------
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// Compute edges of the cut [S*, ~S*]
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std::vector< bool > in_S_star(num_vertices(g), false);
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typename std::vector< vertex_descriptor >::iterator si;
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for (si = S_star.begin(); si != S_star.end(); ++si)
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in_S_star[*si] = true;
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degree_size_type c = 0;
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for (si = S_star.begin(); si != S_star.end(); ++si)
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{
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out_edge_iterator ei, ei_end;
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for (boost::tie(ei, ei_end) = out_edges(*si, g); ei != ei_end; ++ei)
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if (!in_S_star[target(*ei, g)])
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{
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*disconnecting_set++ = *ei;
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++c;
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}
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}
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return c;
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}
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} // namespace boost
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#endif // BOOST_EDGE_CONNECTIVITY
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