File: edge_connectivity.hpp

package info (click to toggle)
boost1.62 1.62.0+dfsg-4
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 686,420 kB
  • sloc: cpp: 2,609,004; xml: 972,558; ansic: 53,674; python: 32,437; sh: 8,829; asm: 3,071; cs: 2,121; makefile: 964; perl: 859; yacc: 472; php: 132; ruby: 94; f90: 55; sql: 13; csh: 6
file content (183 lines) | stat: -rw-r--r-- 6,710 bytes parent folder | download | duplicates (14)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
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