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
|
//=======================================================================
// Copyright 2001 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)
//=======================================================================
#include <boost/config.hpp>
#include <algorithm>
#include <utility>
#include <boost/graph/edmunds_karp_max_flow.hpp>
#include <boost/graph/push_relabel_max_flow.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graphviz.hpp>
namespace boost
{
template < typename Graph >
std::pair < typename graph_traits < Graph >::vertex_descriptor,
typename graph_traits < Graph >::degree_size_type >
min_degree_vertex(Graph & g)
{
typename graph_traits < Graph >::vertex_descriptor p;
typedef typename graph_traits < Graph >::degree_size_type size_type;
size_type delta = (std::numeric_limits < size_type >::max)();
typename graph_traits < Graph >::vertex_iterator i, iend;
for (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 < typename Graph, typename OutputIterator >
void neighbors(const Graph & g,
typename graph_traits < Graph >::vertex_descriptor u,
OutputIterator result)
{
typename graph_traits < Graph >::adjacency_iterator ai, aend;
for (tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai)
*result++ = *ai;
}
template < typename Graph, typename VertexIterator,
typename OutputIterator > void neighbors(const Graph & g,
VertexIterator first,
VertexIterator last,
OutputIterator result)
{
for (; first != last; ++first)
neighbors(g, *first, result);
}
template < typename VertexListGraph, typename OutputIterator >
typename graph_traits < VertexListGraph >::degree_size_type
edge_connectivity(VertexListGraph & g, OutputIterator disconnecting_set)
{
typedef typename graph_traits <
VertexListGraph >::vertex_descriptor vertex_descriptor;
typedef typename graph_traits <
VertexListGraph >::degree_size_type degree_size_type;
typedef color_traits < default_color_type > Color;
typedef typename adjacency_list_traits < vecS, vecS,
directedS >::edge_descriptor edge_descriptor;
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, edge_descriptor > > > > FlowGraph;
vertex_descriptor u, v, p, k;
edge_descriptor e1, e2;
bool inserted;
typename graph_traits < VertexListGraph >::vertex_iterator vi, vi_end;
degree_size_type delta, alpha_star, alpha_S_k;
std::set < vertex_descriptor > S, neighbor_S;
std::vector < vertex_descriptor > S_star, nonneighbor_S;
std::vector < default_color_type > color(num_vertices(g));
std::vector < edge_descriptor > pred(num_vertices(g));
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);
typename graph_traits < VertexListGraph >::edge_iterator ei, ei_end;
for (tie(ei, ei_end) = edges(g); ei != ei_end; ++ei) {
u = source(*ei, g), v = target(*ei, g);
tie(e1, inserted) = add_edge(u, v, flow_g);
cap[e1] = 1;
tie(e2, inserted) = add_edge(v, u, flow_g);
cap[e2] = 1;
rev_edge[e1] = e2;
rev_edge[e2] = e1;
}
tie(p, delta) = min_degree_vertex(g);
S_star.push_back(p);
alpha_star = delta;
S.insert(p);
neighbor_S.insert(p);
neighbors(g, S.begin(), S.end(),
std::inserter(neighbor_S, neighbor_S.begin()));
std::set_difference(vertices(g).first, vertices(g).second,
neighbor_S.begin(), neighbor_S.end(),
std::back_inserter(nonneighbor_S));
while (!nonneighbor_S.empty()) {
k = nonneighbor_S.front();
alpha_S_k = edmunds_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 (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);
neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin()));
nonneighbor_S.clear();
std::set_difference(vertices(g).first, vertices(g).second,
neighbor_S.begin(), neighbor_S.end(),
std::back_inserter(nonneighbor_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) {
typename graph_traits < VertexListGraph >::out_edge_iterator ei, ei_end;
for (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;
}
}
int
main()
{
using namespace boost;
GraphvizGraph g;
read_graphviz("figs/edge-connectivity.dot", g);
typedef graph_traits < GraphvizGraph >::edge_descriptor edge_descriptor;
typedef graph_traits < GraphvizGraph >::degree_size_type degree_size_type;
std::vector < edge_descriptor > disconnecting_set;
degree_size_type c =
edge_connectivity(g, std::back_inserter(disconnecting_set));
std::cout << "The edge connectivity is " << c << "." << std::endl;
property_map < GraphvizGraph, vertex_attribute_t >::type
attr_map = get(vertex_attribute, g);
std::cout << "The disconnecting set is {";
for (std::vector < edge_descriptor >::iterator i =
disconnecting_set.begin(); i != disconnecting_set.end(); ++i)
std::
cout << "(" << attr_map[source(*i, g)]["label"] << "," <<
attr_map[target(*i, g)]["label"] << ") ";
std::cout << "}." << std::endl;
return EXIT_SUCCESS;
}
|
