boost/graph/edmonds_karp_max_flow.hpp

   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 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>
  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   // 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 (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   } // 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