1 | //=======================================================================
|
---|
2 | // Copyright 2000 University of Notre Dame.
|
---|
3 | // Authors: Jeremy G. Siek, Andrew Lumsdaine, Lie-Quan Lee
|
---|
4 | //
|
---|
5 | // Distributed under the Boost Software License, Version 1.0. (See
|
---|
6 | // accompanying file LICENSE_1_0.txt or copy at
|
---|
7 | // http://www.boost.org/LICENSE_1_0.txt)
|
---|
8 | //=======================================================================
|
---|
9 |
|
---|
10 | #ifndef EDMUNDS_KARP_MAX_FLOW_HPP
|
---|
11 | #define EDMUNDS_KARP_MAX_FLOW_HPP
|
---|
12 |
|
---|
13 | #include <boost/config.hpp>
|
---|
14 | #include <vector>
|
---|
15 | #include <algorithm> // for std::min and std::max
|
---|
16 | #include <boost/config.hpp>
|
---|
17 | #include <boost/pending/queue.hpp>
|
---|
18 | #include <boost/property_map.hpp>
|
---|
19 | #include <boost/graph/graph_traits.hpp>
|
---|
20 | #include <boost/graph/properties.hpp>
|
---|
21 | #include <boost/graph/filtered_graph.hpp>
|
---|
22 | #include <boost/graph/breadth_first_search.hpp>
|
---|
23 |
|
---|
24 | namespace boost {
|
---|
25 |
|
---|
26 | // The "labeling" algorithm from "Network Flows" by Ahuja, Magnanti,
|
---|
27 | // Orlin. I think this is the same as or very similar to the original
|
---|
28 | // Edmunds-Karp algorithm. This solves the maximum flow problem.
|
---|
29 |
|
---|
30 | namespace detail {
|
---|
31 |
|
---|
32 | template <class Graph, class ResCapMap>
|
---|
33 | filtered_graph<Graph, is_residual_edge<ResCapMap> >
|
---|
34 | residual_graph(Graph& g, ResCapMap residual_capacity) {
|
---|
35 | return filtered_graph<Graph, is_residual_edge<ResCapMap> >
|
---|
36 | (g, is_residual_edge<ResCapMap>(residual_capacity));
|
---|
37 | }
|
---|
38 |
|
---|
39 | template <class Graph, class PredEdgeMap, class ResCapMap,
|
---|
40 | class RevEdgeMap>
|
---|
41 | inline void
|
---|
42 | augment(Graph& g,
|
---|
43 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
44 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
45 | PredEdgeMap p,
|
---|
46 | ResCapMap residual_capacity,
|
---|
47 | RevEdgeMap reverse_edge)
|
---|
48 | {
|
---|
49 | typename graph_traits<Graph>::edge_descriptor e;
|
---|
50 | typename graph_traits<Graph>::vertex_descriptor u;
|
---|
51 | typedef typename property_traits<ResCapMap>::value_type FlowValue;
|
---|
52 |
|
---|
53 | // find minimum residual capacity along the augmenting path
|
---|
54 | FlowValue delta = (std::numeric_limits<FlowValue>::max)();
|
---|
55 | e = p[sink];
|
---|
56 | do {
|
---|
57 | BOOST_USING_STD_MIN();
|
---|
58 | delta = min BOOST_PREVENT_MACRO_SUBSTITUTION(delta, residual_capacity[e]);
|
---|
59 | u = source(e, g);
|
---|
60 | e = p[u];
|
---|
61 | } while (u != src);
|
---|
62 |
|
---|
63 | // push delta units of flow along the augmenting path
|
---|
64 | e = p[sink];
|
---|
65 | do {
|
---|
66 | residual_capacity[e] -= delta;
|
---|
67 | residual_capacity[reverse_edge[e]] += delta;
|
---|
68 | u = source(e, g);
|
---|
69 | e = p[u];
|
---|
70 | } while (u != src);
|
---|
71 | }
|
---|
72 |
|
---|
73 | } // namespace detail
|
---|
74 |
|
---|
75 | template <class Graph,
|
---|
76 | class CapacityEdgeMap, class ResidualCapacityEdgeMap,
|
---|
77 | class ReverseEdgeMap, class ColorMap, class PredEdgeMap>
|
---|
78 | typename property_traits<CapacityEdgeMap>::value_type
|
---|
79 | edmunds_karp_max_flow
|
---|
80 | (Graph& g,
|
---|
81 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
82 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
83 | CapacityEdgeMap cap,
|
---|
84 | ResidualCapacityEdgeMap res,
|
---|
85 | ReverseEdgeMap rev,
|
---|
86 | ColorMap color,
|
---|
87 | PredEdgeMap pred)
|
---|
88 | {
|
---|
89 | typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
|
---|
90 | typedef typename property_traits<ColorMap>::value_type ColorValue;
|
---|
91 | typedef color_traits<ColorValue> Color;
|
---|
92 |
|
---|
93 | typename graph_traits<Graph>::vertex_iterator u_iter, u_end;
|
---|
94 | typename graph_traits<Graph>::out_edge_iterator ei, e_end;
|
---|
95 | for (tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
|
---|
96 | for (tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
|
---|
97 | res[*ei] = cap[*ei];
|
---|
98 |
|
---|
99 | color[sink] = Color::gray();
|
---|
100 | while (color[sink] != Color::white()) {
|
---|
101 | boost::queue<vertex_t> Q;
|
---|
102 | breadth_first_search
|
---|
103 | (detail::residual_graph(g, res), src, Q,
|
---|
104 | make_bfs_visitor(record_edge_predecessors(pred, on_tree_edge())),
|
---|
105 | color);
|
---|
106 | if (color[sink] != Color::white())
|
---|
107 | detail::augment(g, src, sink, pred, res, rev);
|
---|
108 | } // while
|
---|
109 |
|
---|
110 | typename property_traits<CapacityEdgeMap>::value_type flow = 0;
|
---|
111 | for (tie(ei, e_end) = out_edges(src, g); ei != e_end; ++ei)
|
---|
112 | flow += (cap[*ei] - res[*ei]);
|
---|
113 | return flow;
|
---|
114 | } // edmunds_karp_max_flow()
|
---|
115 |
|
---|
116 | namespace detail {
|
---|
117 | //-------------------------------------------------------------------------
|
---|
118 | // Handle default for color property map
|
---|
119 |
|
---|
120 | // use of class here is a VC++ workaround
|
---|
121 | template <class ColorMap>
|
---|
122 | struct edmunds_karp_dispatch2 {
|
---|
123 | template <class Graph, class PredMap, class P, class T, class R>
|
---|
124 | static typename edge_capacity_value<Graph, P, T, R>::type
|
---|
125 | apply
|
---|
126 | (Graph& g,
|
---|
127 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
128 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
129 | PredMap pred,
|
---|
130 | const bgl_named_params<P, T, R>& params,
|
---|
131 | ColorMap color)
|
---|
132 | {
|
---|
133 | return edmunds_karp_max_flow
|
---|
134 | (g, src, sink,
|
---|
135 | choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
|
---|
136 | choose_pmap(get_param(params, edge_residual_capacity),
|
---|
137 | g, edge_residual_capacity),
|
---|
138 | choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
|
---|
139 | color, pred);
|
---|
140 | }
|
---|
141 | };
|
---|
142 | template<>
|
---|
143 | struct edmunds_karp_dispatch2<detail::error_property_not_found> {
|
---|
144 | template <class Graph, class PredMap, class P, class T, class R>
|
---|
145 | static typename edge_capacity_value<Graph, P, T, R>::type
|
---|
146 | apply
|
---|
147 | (Graph& g,
|
---|
148 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
149 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
150 | PredMap pred,
|
---|
151 | const bgl_named_params<P, T, R>& params,
|
---|
152 | detail::error_property_not_found)
|
---|
153 | {
|
---|
154 | typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
|
---|
155 | typedef typename graph_traits<Graph>::vertices_size_type size_type;
|
---|
156 | size_type n = is_default_param(get_param(params, vertex_color)) ?
|
---|
157 | num_vertices(g) : 1;
|
---|
158 | std::vector<default_color_type> color_vec(n);
|
---|
159 | return edmunds_karp_max_flow
|
---|
160 | (g, src, sink,
|
---|
161 | choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
|
---|
162 | choose_pmap(get_param(params, edge_residual_capacity),
|
---|
163 | g, edge_residual_capacity),
|
---|
164 | choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
|
---|
165 | make_iterator_property_map(color_vec.begin(), choose_const_pmap
|
---|
166 | (get_param(params, vertex_index),
|
---|
167 | g, vertex_index), color_vec[0]),
|
---|
168 | pred);
|
---|
169 | }
|
---|
170 | };
|
---|
171 |
|
---|
172 | //-------------------------------------------------------------------------
|
---|
173 | // Handle default for predecessor property map
|
---|
174 |
|
---|
175 | // use of class here is a VC++ workaround
|
---|
176 | template <class PredMap>
|
---|
177 | struct edmunds_karp_dispatch1 {
|
---|
178 | template <class Graph, class P, class T, class R>
|
---|
179 | static typename edge_capacity_value<Graph, P, T, R>::type
|
---|
180 | apply(Graph& g,
|
---|
181 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
182 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
183 | const bgl_named_params<P, T, R>& params,
|
---|
184 | PredMap pred)
|
---|
185 | {
|
---|
186 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
|
---|
187 | return edmunds_karp_dispatch2<C>::apply
|
---|
188 | (g, src, sink, pred, params, get_param(params, vertex_color));
|
---|
189 | }
|
---|
190 | };
|
---|
191 | template<>
|
---|
192 | struct edmunds_karp_dispatch1<detail::error_property_not_found> {
|
---|
193 |
|
---|
194 | template <class Graph, class P, class T, class R>
|
---|
195 | static typename edge_capacity_value<Graph, P, T, R>::type
|
---|
196 | apply
|
---|
197 | (Graph& g,
|
---|
198 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
199 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
200 | const bgl_named_params<P, T, R>& params,
|
---|
201 | detail::error_property_not_found)
|
---|
202 | {
|
---|
203 | typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
|
---|
204 | typedef typename graph_traits<Graph>::vertices_size_type size_type;
|
---|
205 | size_type n = is_default_param(get_param(params, vertex_predecessor)) ?
|
---|
206 | num_vertices(g) : 1;
|
---|
207 | std::vector<edge_descriptor> pred_vec(n);
|
---|
208 |
|
---|
209 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
|
---|
210 | return edmunds_karp_dispatch2<C>::apply
|
---|
211 | (g, src, sink,
|
---|
212 | make_iterator_property_map(pred_vec.begin(), choose_const_pmap
|
---|
213 | (get_param(params, vertex_index),
|
---|
214 | g, vertex_index), pred_vec[0]),
|
---|
215 | params,
|
---|
216 | get_param(params, vertex_color));
|
---|
217 | }
|
---|
218 | };
|
---|
219 |
|
---|
220 | } // namespace detail
|
---|
221 |
|
---|
222 | template <class Graph, class P, class T, class R>
|
---|
223 | typename detail::edge_capacity_value<Graph, P, T, R>::type
|
---|
224 | edmunds_karp_max_flow
|
---|
225 | (Graph& g,
|
---|
226 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
227 | typename graph_traits<Graph>::vertex_descriptor sink,
|
---|
228 | const bgl_named_params<P, T, R>& params)
|
---|
229 | {
|
---|
230 | typedef typename property_value< bgl_named_params<P,T,R>, vertex_predecessor_t>::type Pred;
|
---|
231 | return detail::edmunds_karp_dispatch1<Pred>::apply
|
---|
232 | (g, src, sink, params, get_param(params, vertex_predecessor));
|
---|
233 | }
|
---|
234 |
|
---|
235 | template <class Graph>
|
---|
236 | typename property_traits<
|
---|
237 | typename property_map<Graph, edge_capacity_t>::const_type
|
---|
238 | >::value_type
|
---|
239 | edmunds_karp_max_flow
|
---|
240 | (Graph& g,
|
---|
241 | typename graph_traits<Graph>::vertex_descriptor src,
|
---|
242 | typename graph_traits<Graph>::vertex_descriptor sink)
|
---|
243 | {
|
---|
244 | bgl_named_params<int, buffer_param_t> params(0);
|
---|
245 | return edmunds_karp_max_flow(g, src, sink, params);
|
---|
246 | }
|
---|
247 |
|
---|
248 | } // namespace boost
|
---|
249 |
|
---|
250 | #endif // EDMUNDS_KARP_MAX_FLOW_HPP
|
---|