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edmonds_karp_max_flow.hpp
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edmonds_karp_max_flow.hpp
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//=======================================================================
// 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 (tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
for (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 (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