Chris@16: //=======================================================================
Chris@16: // Copyright 2000 University of Notre Dame.
Chris@16: // Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee
Chris@16: //
Chris@16: // Distributed under the Boost Software License, Version 1.0. (See
Chris@16: // accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: //=======================================================================
Chris@16: 
Chris@16: #ifndef BOOST_EDGE_CONNECTIVITY
Chris@16: #define BOOST_EDGE_CONNECTIVITY
Chris@16: 
Chris@16: // WARNING: not-yet fully tested!
Chris@16: 
Chris@16: #include <boost/config.hpp>
Chris@16: #include <vector>
Chris@16: #include <set>
Chris@16: #include <algorithm>
Chris@16: #include <boost/graph/edmonds_karp_max_flow.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   namespace detail {
Chris@16: 
Chris@16:     template <class Graph>
Chris@16:     inline
Chris@16:     std::pair<typename graph_traits<Graph>::vertex_descriptor,
Chris@16:               typename graph_traits<Graph>::degree_size_type>
Chris@16:     min_degree_vertex(Graph& g)
Chris@16:     {
Chris@16:       typedef graph_traits<Graph> Traits;
Chris@16:       typename Traits::vertex_descriptor p;
Chris@16:       typedef typename Traits::degree_size_type size_type;
Chris@16:       size_type delta = (std::numeric_limits<size_type>::max)();
Chris@16: 
Chris@16:       typename Traits::vertex_iterator i, iend;
Chris@16:       for (boost::tie(i, iend) = vertices(g); i != iend; ++i)
Chris@16:         if (degree(*i, g) < delta) {
Chris@16:           delta = degree(*i, g);
Chris@16:           p = *i;
Chris@16:         }
Chris@16:       return std::make_pair(p, delta);
Chris@16:     }
Chris@16: 
Chris@16:     template <class Graph, class OutputIterator>
Chris@16:     void neighbors(const Graph& g, 
Chris@16:                    typename graph_traits<Graph>::vertex_descriptor u,
Chris@16:                    OutputIterator result)
Chris@16:     {
Chris@16:       typename graph_traits<Graph>::adjacency_iterator ai, aend;
Chris@16:       for (boost::tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)
Chris@16:         *result++ = *ai;
Chris@16:     }
Chris@16: 
Chris@16:     template <class Graph, class VertexIterator, class OutputIterator>
Chris@16:     void neighbors(const Graph& g, 
Chris@16:                    VertexIterator first, VertexIterator last,
Chris@16:                    OutputIterator result)
Chris@16:     {
Chris@16:       for (; first != last; ++first)
Chris@16:         neighbors(g, *first, result);
Chris@16:     }
Chris@16: 
Chris@16:   } // namespace detail
Chris@16: 
Chris@16:   // O(m n)
Chris@16:   template <class VertexListGraph, class OutputIterator>
Chris@16:   typename graph_traits<VertexListGraph>::degree_size_type
Chris@16:   edge_connectivity(VertexListGraph& g, OutputIterator disconnecting_set)
Chris@16:   {
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // Type Definitions
Chris@16:     typedef graph_traits<VertexListGraph> Traits;
Chris@16:     typedef typename Traits::vertex_iterator vertex_iterator;
Chris@16:     typedef typename Traits::edge_iterator edge_iterator;
Chris@16:     typedef typename Traits::out_edge_iterator out_edge_iterator;
Chris@16:     typedef typename Traits::vertex_descriptor vertex_descriptor;
Chris@16:     typedef typename Traits::degree_size_type degree_size_type;
Chris@16:     typedef color_traits<default_color_type> Color;
Chris@16: 
Chris@16:     typedef adjacency_list_traits<vecS, vecS, directedS> Tr;
Chris@16:     typedef typename Tr::edge_descriptor Tr_edge_desc;
Chris@16:     typedef adjacency_list<vecS, vecS, directedS, no_property, 
Chris@16:       property<edge_capacity_t, degree_size_type,
Chris@16:         property<edge_residual_capacity_t, degree_size_type,
Chris@16:           property<edge_reverse_t, Tr_edge_desc> > > > 
Chris@16:       FlowGraph;
Chris@16:     typedef typename graph_traits<FlowGraph>::edge_descriptor edge_descriptor;
Chris@16: 
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // Variable Declarations
Chris@16:     vertex_descriptor u, v, p, k;
Chris@16:     edge_descriptor e1, e2;
Chris@16:     bool inserted;
Chris@16:     vertex_iterator vi, vi_end;
Chris@16:     edge_iterator ei, ei_end;
Chris@16:     degree_size_type delta, alpha_star, alpha_S_k;
Chris@16:     std::set<vertex_descriptor> S, neighbor_S;
Chris@16:     std::vector<vertex_descriptor> S_star, non_neighbor_S;
Chris@16:     std::vector<default_color_type> color(num_vertices(g));
Chris@16:     std::vector<edge_descriptor> pred(num_vertices(g));
Chris@16: 
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // Create a network flow graph out of the undirected graph
Chris@16:     FlowGraph flow_g(num_vertices(g));
Chris@16: 
Chris@16:     typename property_map<FlowGraph, edge_capacity_t>::type
Chris@16:       cap = get(edge_capacity, flow_g);
Chris@16:     typename property_map<FlowGraph, edge_residual_capacity_t>::type
Chris@16:       res_cap = get(edge_residual_capacity, flow_g);
Chris@16:     typename property_map<FlowGraph, edge_reverse_t>::type
Chris@16:       rev_edge = get(edge_reverse, flow_g);
Chris@16: 
Chris@16:     for (boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei) {
Chris@16:       u = source(*ei, g), v = target(*ei, g);
Chris@16:       boost::tie(e1, inserted) = add_edge(u, v, flow_g);
Chris@16:       cap[e1] = 1;
Chris@16:       boost::tie(e2, inserted) = add_edge(v, u, flow_g);
Chris@16:       cap[e2] = 1; // not sure about this
Chris@16:       rev_edge[e1] = e2;
Chris@16:       rev_edge[e2] = e1;
Chris@16:     }
Chris@16: 
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // The Algorithm
Chris@16: 
Chris@16:     boost::tie(p, delta) = detail::min_degree_vertex(g);
Chris@16:     S_star.push_back(p);
Chris@16:     alpha_star = delta;
Chris@16:     S.insert(p);
Chris@16:     neighbor_S.insert(p);
Chris@16:     detail::neighbors(g, S.begin(), S.end(), 
Chris@16:                       std::inserter(neighbor_S, neighbor_S.begin()));
Chris@16: 
Chris@16:     boost::tie(vi, vi_end) = vertices(g);
Chris@16:     std::set_difference(vi, vi_end,
Chris@16:                         neighbor_S.begin(), neighbor_S.end(),
Chris@16:                         std::back_inserter(non_neighbor_S));
Chris@16: 
Chris@16:     while (!non_neighbor_S.empty()) { // at most n - 1 times
Chris@16:       k = non_neighbor_S.front();
Chris@16: 
Chris@16:       alpha_S_k = edmonds_karp_max_flow
Chris@16:         (flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]);
Chris@16: 
Chris@16:       if (alpha_S_k < alpha_star) {
Chris@16:         alpha_star = alpha_S_k;
Chris@16:         S_star.clear();
Chris@16:         for (boost::tie(vi, vi_end) = vertices(flow_g); vi != vi_end; ++vi)
Chris@16:           if (color[*vi] != Color::white())
Chris@16:             S_star.push_back(*vi);
Chris@16:       }
Chris@16:       S.insert(k);
Chris@16:       neighbor_S.insert(k);
Chris@16:       detail::neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));
Chris@16:       non_neighbor_S.clear();
Chris@16:       boost::tie(vi, vi_end) = vertices(g);
Chris@16:       std::set_difference(vi, vi_end,
Chris@16:                           neighbor_S.begin(), neighbor_S.end(),
Chris@16:                           std::back_inserter(non_neighbor_S));
Chris@16:     }
Chris@16:     //-------------------------------------------------------------------------
Chris@16:     // Compute edges of the cut [S*, ~S*]
Chris@16:     std::vector<bool> in_S_star(num_vertices(g), false);
Chris@16:     typename std::vector<vertex_descriptor>::iterator si;
Chris@16:     for (si = S_star.begin(); si != S_star.end(); ++si)
Chris@16:       in_S_star[*si] = true;
Chris@16: 
Chris@16:     degree_size_type c = 0;
Chris@16:     for (si = S_star.begin(); si != S_star.end(); ++si) {
Chris@16:       out_edge_iterator ei, ei_end;
Chris@16:       for (boost::tie(ei, ei_end) = out_edges(*si, g); ei != ei_end; ++ei)
Chris@16:         if (!in_S_star[target(*ei, g)]) {
Chris@16:           *disconnecting_set++ = *ei;
Chris@16:           ++c;
Chris@16:         }
Chris@16:     }
Chris@16:     return c;
Chris@16:   }
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_EDGE_CONNECTIVITY