Added boost header

test/external/boost/graph/edge_connectivity.hpp

@@ -0,0 +1,183 @@
+//=======================================================================
+// 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