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