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183 lines
6.6 KiB
183 lines
6.6 KiB
//======================================================================= |
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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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namespace detail { |
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template <class Graph> |
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inline |
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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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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, |
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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 |
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edge_connectivity(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 |
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cap = get(edge_capacity, flow_g); |
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typename property_map<FlowGraph, edge_residual_capacity_t>::type |
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res_cap = get(edge_residual_capacity, flow_g); |
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typename property_map<FlowGraph, edge_reverse_t>::type |
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rev_edge = 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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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(g, S.begin(), S.end(), |
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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, |
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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()) { // 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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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, |
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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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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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*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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