| //======================================================================= | |
| // 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 |