1 | //======================================================================= |
---|
2 | // Copyright 2001 Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee, |
---|
3 | // |
---|
4 | // Distributed under the Boost Software License, Version 1.0. (See |
---|
5 | // accompanying file LICENSE_1_0.txt or copy at |
---|
6 | // http://www.boost.org/LICENSE_1_0.txt) |
---|
7 | //======================================================================= |
---|
8 | #include <boost/config.hpp> |
---|
9 | #include <algorithm> |
---|
10 | #include <utility> |
---|
11 | #include <boost/graph/edmunds_karp_max_flow.hpp> |
---|
12 | #include <boost/graph/push_relabel_max_flow.hpp> |
---|
13 | #include <boost/graph/adjacency_list.hpp> |
---|
14 | #include <boost/graph/graphviz.hpp> |
---|
15 | |
---|
16 | namespace boost |
---|
17 | { |
---|
18 | template < typename Graph > |
---|
19 | std::pair < typename graph_traits < Graph >::vertex_descriptor, |
---|
20 | typename graph_traits < Graph >::degree_size_type > |
---|
21 | min_degree_vertex(Graph & g) |
---|
22 | { |
---|
23 | typename graph_traits < Graph >::vertex_descriptor p; |
---|
24 | typedef typename graph_traits < Graph >::degree_size_type size_type; |
---|
25 | size_type delta = (std::numeric_limits < size_type >::max)(); |
---|
26 | typename graph_traits < Graph >::vertex_iterator i, iend; |
---|
27 | for (tie(i, iend) = vertices(g); i != iend; ++i) |
---|
28 | if (degree(*i, g) < delta) |
---|
29 | { |
---|
30 | delta = degree(*i, g); |
---|
31 | p = *i; |
---|
32 | } |
---|
33 | return std::make_pair(p, delta); |
---|
34 | } |
---|
35 | |
---|
36 | template < typename Graph, typename OutputIterator > |
---|
37 | void neighbors(const Graph & g, |
---|
38 | typename graph_traits < Graph >::vertex_descriptor u, |
---|
39 | OutputIterator result) |
---|
40 | { |
---|
41 | typename graph_traits < Graph >::adjacency_iterator ai, aend; |
---|
42 | for (tie(ai, aend) = adjacent_vertices(u, g); ai != aend; ++ai) |
---|
43 | *result++ = *ai; |
---|
44 | } |
---|
45 | template < typename Graph, typename VertexIterator, |
---|
46 | typename OutputIterator > void neighbors(const Graph & g, |
---|
47 | VertexIterator first, |
---|
48 | VertexIterator last, |
---|
49 | OutputIterator result) |
---|
50 | { |
---|
51 | for (; first != last; ++first) |
---|
52 | neighbors(g, *first, result); |
---|
53 | } |
---|
54 | |
---|
55 | template < typename VertexListGraph, typename OutputIterator > |
---|
56 | typename graph_traits < VertexListGraph >::degree_size_type |
---|
57 | edge_connectivity(VertexListGraph & g, OutputIterator disconnecting_set) |
---|
58 | { |
---|
59 | typedef typename graph_traits < |
---|
60 | VertexListGraph >::vertex_descriptor vertex_descriptor; |
---|
61 | typedef typename graph_traits < |
---|
62 | VertexListGraph >::degree_size_type degree_size_type; |
---|
63 | typedef color_traits < default_color_type > Color; |
---|
64 | typedef typename adjacency_list_traits < vecS, vecS, |
---|
65 | directedS >::edge_descriptor edge_descriptor; |
---|
66 | typedef adjacency_list < vecS, vecS, directedS, no_property, |
---|
67 | property < edge_capacity_t, degree_size_type, |
---|
68 | property < edge_residual_capacity_t, degree_size_type, |
---|
69 | property < edge_reverse_t, edge_descriptor > > > > FlowGraph; |
---|
70 | |
---|
71 | vertex_descriptor u, v, p, k; |
---|
72 | edge_descriptor e1, e2; |
---|
73 | bool inserted; |
---|
74 | typename graph_traits < VertexListGraph >::vertex_iterator vi, vi_end; |
---|
75 | degree_size_type delta, alpha_star, alpha_S_k; |
---|
76 | std::set < vertex_descriptor > S, neighbor_S; |
---|
77 | std::vector < vertex_descriptor > S_star, nonneighbor_S; |
---|
78 | std::vector < default_color_type > color(num_vertices(g)); |
---|
79 | std::vector < edge_descriptor > pred(num_vertices(g)); |
---|
80 | |
---|
81 | FlowGraph flow_g(num_vertices(g)); |
---|
82 | typename property_map < FlowGraph, edge_capacity_t >::type |
---|
83 | cap = get(edge_capacity, flow_g); |
---|
84 | typename property_map < FlowGraph, edge_residual_capacity_t >::type |
---|
85 | res_cap = get(edge_residual_capacity, flow_g); |
---|
86 | typename property_map < FlowGraph, edge_reverse_t >::type |
---|
87 | rev_edge = get(edge_reverse, flow_g); |
---|
88 | |
---|
89 | typename graph_traits < VertexListGraph >::edge_iterator ei, ei_end; |
---|
90 | for (tie(ei, ei_end) = edges(g); ei != ei_end; ++ei) { |
---|
91 | u = source(*ei, g), v = target(*ei, g); |
---|
92 | tie(e1, inserted) = add_edge(u, v, flow_g); |
---|
93 | cap[e1] = 1; |
---|
94 | tie(e2, inserted) = add_edge(v, u, flow_g); |
---|
95 | cap[e2] = 1; |
---|
96 | rev_edge[e1] = e2; |
---|
97 | rev_edge[e2] = e1; |
---|
98 | } |
---|
99 | |
---|
100 | tie(p, delta) = min_degree_vertex(g); |
---|
101 | S_star.push_back(p); |
---|
102 | alpha_star = delta; |
---|
103 | S.insert(p); |
---|
104 | neighbor_S.insert(p); |
---|
105 | neighbors(g, S.begin(), S.end(), |
---|
106 | std::inserter(neighbor_S, neighbor_S.begin())); |
---|
107 | std::set_difference(vertices(g).first, vertices(g).second, |
---|
108 | neighbor_S.begin(), neighbor_S.end(), |
---|
109 | std::back_inserter(nonneighbor_S)); |
---|
110 | |
---|
111 | while (!nonneighbor_S.empty()) { |
---|
112 | k = nonneighbor_S.front(); |
---|
113 | alpha_S_k = edmunds_karp_max_flow |
---|
114 | (flow_g, p, k, cap, res_cap, rev_edge, &color[0], &pred[0]); |
---|
115 | if (alpha_S_k < alpha_star) { |
---|
116 | alpha_star = alpha_S_k; |
---|
117 | S_star.clear(); |
---|
118 | for (tie(vi, vi_end) = vertices(flow_g); vi != vi_end; ++vi) |
---|
119 | if (color[*vi] != Color::white()) |
---|
120 | S_star.push_back(*vi); |
---|
121 | } |
---|
122 | S.insert(k); |
---|
123 | neighbor_S.insert(k); |
---|
124 | neighbors(g, k, std::inserter(neighbor_S, neighbor_S.begin())); |
---|
125 | nonneighbor_S.clear(); |
---|
126 | std::set_difference(vertices(g).first, vertices(g).second, |
---|
127 | neighbor_S.begin(), neighbor_S.end(), |
---|
128 | std::back_inserter(nonneighbor_S)); |
---|
129 | } |
---|
130 | |
---|
131 | std::vector < bool > in_S_star(num_vertices(g), false); |
---|
132 | typename std::vector < vertex_descriptor >::iterator si; |
---|
133 | for (si = S_star.begin(); si != S_star.end(); ++si) |
---|
134 | in_S_star[*si] = true; |
---|
135 | degree_size_type c = 0; |
---|
136 | for (si = S_star.begin(); si != S_star.end(); ++si) { |
---|
137 | typename graph_traits < VertexListGraph >::out_edge_iterator ei, ei_end; |
---|
138 | for (tie(ei, ei_end) = out_edges(*si, g); ei != ei_end; ++ei) |
---|
139 | if (!in_S_star[target(*ei, g)]) { |
---|
140 | *disconnecting_set++ = *ei; |
---|
141 | ++c; |
---|
142 | } |
---|
143 | } |
---|
144 | |
---|
145 | return c; |
---|
146 | } |
---|
147 | |
---|
148 | } |
---|
149 | |
---|
150 | int |
---|
151 | main() |
---|
152 | { |
---|
153 | using namespace boost; |
---|
154 | GraphvizGraph g; |
---|
155 | read_graphviz("figs/edge-connectivity.dot", g); |
---|
156 | |
---|
157 | typedef graph_traits < GraphvizGraph >::edge_descriptor edge_descriptor; |
---|
158 | typedef graph_traits < GraphvizGraph >::degree_size_type degree_size_type; |
---|
159 | std::vector < edge_descriptor > disconnecting_set; |
---|
160 | degree_size_type c = |
---|
161 | edge_connectivity(g, std::back_inserter(disconnecting_set)); |
---|
162 | |
---|
163 | std::cout << "The edge connectivity is " << c << "." << std::endl; |
---|
164 | |
---|
165 | property_map < GraphvizGraph, vertex_attribute_t >::type |
---|
166 | attr_map = get(vertex_attribute, g); |
---|
167 | |
---|
168 | std::cout << "The disconnecting set is {"; |
---|
169 | for (std::vector < edge_descriptor >::iterator i = |
---|
170 | disconnecting_set.begin(); i != disconnecting_set.end(); ++i) |
---|
171 | std:: |
---|
172 | cout << "(" << attr_map[source(*i, g)]["label"] << "," << |
---|
173 | attr_map[target(*i, g)]["label"] << ") "; |
---|
174 | std::cout << "}." << std::endl; |
---|
175 | return EXIT_SUCCESS; |
---|
176 | } |
---|