#### /Src/Dependencies/Boost/boost/graph/edmonds_karp_max_flow.hpp

C++ Header | 250 lines | 206 code | 25 blank | 19 comment | 14 complexity | c188ac58da2f39a90c404481f1492a4e MD5 | raw file
```  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
8//=======================================================================
9
10#ifndef EDMONDS_KARP_MAX_FLOW_HPP
11#define EDMONDS_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/property_map.hpp>
19#include <boost/graph/graph_traits.hpp>
20#include <boost/graph/properties.hpp>
21#include <boost/graph/filtered_graph.hpp>
23
24namespace 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  // Edmonds-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  edmonds_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 (boost::tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
96      for (boost::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;
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 (boost::tie(ei, e_end) = out_edges(src, g); ei != e_end; ++ei)
112      flow += (cap[*ei] - res[*ei]);
113    return flow;
114  } // edmonds_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 edmonds_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 edmonds_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 edmonds_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 edmonds_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 edmonds_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 edmonds_karp_dispatch2<C>::apply
188          (g, src, sink, pred, params, get_param(params, vertex_color));
189      }
190    };
191    template<>
192    struct edmonds_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 edmonds_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  edmonds_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::edmonds_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  edmonds_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 edmonds_karp_max_flow(g, src, sink, params);
246  }
247
248} // namespace boost
249
250#endif // EDMONDS_KARP_MAX_FLOW_HPP
```