| //======================================================================= | |
| // 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 |