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