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boost/graph/edmonds_karp_max_flow.hpp

//=======================================================================
// Copyright 2000 University of Notre Dame.
// Authors: 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)
//=======================================================================

#ifndef EDMONDS_KARP_MAX_FLOW_HPP
#define EDMONDS_KARP_MAX_FLOW_HPP

#include <boost/config.hpp>
#include <vector>
#include <algorithm> // for std::min and std::max
#include <boost/config.hpp>
#include <boost/pending/queue.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/properties.hpp>
#include <boost/graph/filtered_graph.hpp>
#include <boost/graph/breadth_first_search.hpp>

namespace boost {

  // The "labeling" algorithm from "Network Flows" by Ahuja, Magnanti,
  // Orlin.  I think this is the same as or very similar to the original
  // Edmonds-Karp algorithm.  This solves the maximum flow problem.

  namespace detail {

    template <class Graph, class ResCapMap>
    filtered_graph<Graph, is_residual_edge<ResCapMap> >
    residual_graph(Graph& g, ResCapMap residual_capacity) {
      return filtered_graph<Graph, is_residual_edge<ResCapMap> >
        (g, is_residual_edge<ResCapMap>(residual_capacity));
    }

    template <class Graph, class PredEdgeMap, class ResCapMap,
              class RevEdgeMap>
    inline void
    augment(Graph& g, 
            typename graph_traits<Graph>::vertex_descriptor src,
            typename graph_traits<Graph>::vertex_descriptor sink,
            PredEdgeMap p, 
            ResCapMap residual_capacity,
            RevEdgeMap reverse_edge)
    {
      typename graph_traits<Graph>::edge_descriptor e;
      typename graph_traits<Graph>::vertex_descriptor u;
      typedef typename property_traits<ResCapMap>::value_type FlowValue;

      // find minimum residual capacity along the augmenting path
      FlowValue delta = (std::numeric_limits<FlowValue>::max)();
      e = p[sink];
      do {
        BOOST_USING_STD_MIN();
        delta = min BOOST_PREVENT_MACRO_SUBSTITUTION(delta, residual_capacity[e]);
        u = source(e, g);
        e = p[u];
      } while (u != src);

      // push delta units of flow along the augmenting path
      e = p[sink];
      do {
        residual_capacity[e] -= delta;
        residual_capacity[reverse_edge[e]] += delta;
        u = source(e, g);
        e = p[u];
      } while (u != src);
    }

  } // namespace detail

  template <class Graph, 
            class CapacityEdgeMap, class ResidualCapacityEdgeMap,
            class ReverseEdgeMap, class ColorMap, class PredEdgeMap>
  typename property_traits<CapacityEdgeMap>::value_type
  edmonds_karp_max_flow
    (Graph& g, 
     typename graph_traits<Graph>::vertex_descriptor src,
     typename graph_traits<Graph>::vertex_descriptor sink,
     CapacityEdgeMap cap, 
     ResidualCapacityEdgeMap res,
     ReverseEdgeMap rev, 
     ColorMap color, 
     PredEdgeMap pred)
  {
    typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
    typedef typename property_traits<ColorMap>::value_type ColorValue;
    typedef color_traits<ColorValue> Color;
    
    typename graph_traits<Graph>::vertex_iterator u_iter, u_end;
    typename graph_traits<Graph>::out_edge_iterator ei, e_end;
    for (boost::tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
      for (boost::tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
        res[*ei] = cap[*ei];
    
    color[sink] = Color::gray();
    while (color[sink] != Color::white()) {
      boost::queue<vertex_t> Q;
      breadth_first_search
        (detail::residual_graph(g, res), src, Q,
         make_bfs_visitor(record_edge_predecessors(pred, on_tree_edge())),
         color);
      if (color[sink] != Color::white())
        detail::augment(g, src, sink, pred, res, rev);
    } // while
    
    typename property_traits<CapacityEdgeMap>::value_type flow = 0;
    for (boost::tie(ei, e_end) = out_edges(src, g); ei != e_end; ++ei)
      flow += (cap[*ei] - res[*ei]);
    return flow;
  } // edmonds_karp_max_flow()
  
  namespace detail {
    //-------------------------------------------------------------------------
    // Handle default for color property map

    // use of class here is a VC++ workaround
    template <class ColorMap>
    struct edmonds_karp_dispatch2 {
      template <class Graph, class PredMap, class P, class T, class R>
      static typename edge_capacity_value<Graph, P, T, R>::type
      apply
      (Graph& g,
       typename graph_traits<Graph>::vertex_descriptor src,
       typename graph_traits<Graph>::vertex_descriptor sink,
       PredMap pred,
       const bgl_named_params<P, T, R>& params,
       ColorMap color)
      {
        return edmonds_karp_max_flow
          (g, src, sink, 
           choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
           choose_pmap(get_param(params, edge_residual_capacity), 
                       g, edge_residual_capacity),
           choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
           color, pred);
      }
    };
    template<>
    struct edmonds_karp_dispatch2<detail::error_property_not_found> {
      template <class Graph, class PredMap, class P, class T, class R>
      static typename edge_capacity_value<Graph, P, T, R>::type
      apply
      (Graph& g,
       typename graph_traits<Graph>::vertex_descriptor src,
       typename graph_traits<Graph>::vertex_descriptor sink,
       PredMap pred,
       const bgl_named_params<P, T, R>& params,
       detail::error_property_not_found)
      {
        typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
        typedef typename graph_traits<Graph>::vertices_size_type size_type;
        size_type n = is_default_param(get_param(params, vertex_color)) ?
          num_vertices(g) : 1;
        std::vector<default_color_type> color_vec(n);
        return edmonds_karp_max_flow
          (g, src, sink, 
           choose_const_pmap(get_param(params, edge_capacity), g, edge_capacity),
           choose_pmap(get_param(params, edge_residual_capacity), 
                       g, edge_residual_capacity),
           choose_const_pmap(get_param(params, edge_reverse), g, edge_reverse),
           make_iterator_property_map(color_vec.begin(), choose_const_pmap
                                      (get_param(params, vertex_index),
                                       g, vertex_index), color_vec[0]),
           pred);
      }
    };

    //-------------------------------------------------------------------------
    // Handle default for predecessor property map

    // use of class here is a VC++ workaround
    template <class PredMap>
    struct edmonds_karp_dispatch1 {
      template <class Graph, class P, class T, class R>
      static typename edge_capacity_value<Graph, P, T, R>::type
      apply(Graph& g,
            typename graph_traits<Graph>::vertex_descriptor src,
            typename graph_traits<Graph>::vertex_descriptor sink,
            const bgl_named_params<P, T, R>& params,
            PredMap pred)
      {
        typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
        return edmonds_karp_dispatch2<C>::apply
          (g, src, sink, pred, params, get_param(params, vertex_color));
      }
    };
    template<>
    struct edmonds_karp_dispatch1<detail::error_property_not_found> {

      template <class Graph, class P, class T, class R>
      static typename edge_capacity_value<Graph, P, T, R>::type
      apply
      (Graph& g,
       typename graph_traits<Graph>::vertex_descriptor src,
       typename graph_traits<Graph>::vertex_descriptor sink,
       const bgl_named_params<P, T, R>& params,
       detail::error_property_not_found)
      {
        typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor;
        typedef typename graph_traits<Graph>::vertices_size_type size_type;
        size_type n = is_default_param(get_param(params, vertex_predecessor)) ?
          num_vertices(g) : 1;
        std::vector<edge_descriptor> pred_vec(n);
        
        typedef typename property_value< bgl_named_params<P,T,R>, vertex_color_t>::type C;
        return edmonds_karp_dispatch2<C>::apply
          (g, src, sink, 
           make_iterator_property_map(pred_vec.begin(), choose_const_pmap
                                      (get_param(params, vertex_index),
                                       g, vertex_index), pred_vec[0]),
           params, 
           get_param(params, vertex_color));
      }
    };
    
  } // namespace detail

  template <class Graph, class P, class T, class R>
  typename detail::edge_capacity_value<Graph, P, T, R>::type
  edmonds_karp_max_flow
    (Graph& g,
     typename graph_traits<Graph>::vertex_descriptor src,
     typename graph_traits<Graph>::vertex_descriptor sink,
     const bgl_named_params<P, T, R>& params)
  {
    typedef typename property_value< bgl_named_params<P,T,R>, vertex_predecessor_t>::type Pred;
    return detail::edmonds_karp_dispatch1<Pred>::apply
      (g, src, sink, params, get_param(params, vertex_predecessor));
  }

  template <class Graph>
  typename property_traits<
    typename property_map<Graph, edge_capacity_t>::const_type
  >::value_type
  edmonds_karp_max_flow
    (Graph& g,
     typename graph_traits<Graph>::vertex_descriptor src,
     typename graph_traits<Graph>::vertex_descriptor sink)
  {
    bgl_named_params<int, buffer_param_t> params(0);
    return edmonds_karp_max_flow(g, src, sink, params);
  }

} // namespace boost

#endif // EDMONDS_KARP_MAX_FLOW_HPP