A strange compilation failure (under cygwin) is fixed.
Version 0.3 should be fixed as well.
2 * src/lemon/min_cost_flow.h - Part of LEMON, a generic C++ optimization library
4 * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
5 * (Egervary Combinatorial Optimization Research Group, EGRES).
7 * Permission to use, modify and distribute this software is granted
8 * provided that this copyright notice appears in all copies. For
9 * precise terms see the accompanying LICENSE file.
11 * This software is provided "AS IS" with no warranty of any kind,
12 * express or implied, and with no claim as to its suitability for any
17 #ifndef LEMON_MIN_COST_FLOW_H
18 #define LEMON_MIN_COST_FLOW_H
22 ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost
25 #include <lemon/dijkstra.h>
26 #include <lemon/graph_wrapper.h>
27 #include <lemon/maps.h>
32 /// \addtogroup flowalgs
35 ///\brief Implementation of an algorithm for finding a flow of value \c k
36 ///(for small values of \c k) having minimal total cost between 2 nodes
39 /// The class \ref lemon::MinCostFlow "MinCostFlow" implements
40 /// an algorithm for finding a flow of value \c k
41 /// having minimal total cost
42 /// from a given source node to a given target node in an
43 /// edge-weighted directed graph. To this end,
44 /// the edge-capacities and edge-weitghs have to be nonnegative.
45 /// The edge-capacities should be integers, but the edge-weights can be
46 /// integers, reals or of other comparable numeric type.
47 /// This algorithm is intended to use only for small values of \c k,
48 /// since it is only polynomial in k,
49 /// not in the length of k (which is log k).
50 /// In order to find the minimum cost flow of value \c k it
51 /// finds the minimum cost flow of value \c i for every
52 /// \c i between 0 and \c k.
54 ///\param Graph The directed graph type the algorithm runs on.
55 ///\param LengthMap The type of the length map.
56 ///\param CapacityMap The capacity map type.
58 ///\author Attila Bernath
59 template <typename Graph, typename LengthMap, typename CapacityMap>
62 typedef typename LengthMap::Value Length;
64 //Warning: this should be integer type
65 typedef typename CapacityMap::Value Capacity;
67 typedef typename Graph::Node Node;
68 typedef typename Graph::NodeIt NodeIt;
69 typedef typename Graph::Edge Edge;
70 typedef typename Graph::OutEdgeIt OutEdgeIt;
71 typedef typename Graph::template EdgeMap<int> EdgeIntMap;
73 typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGW;
74 typedef typename ResGW::Edge ResGraphEdge;
79 const LengthMap& length;
80 const CapacityMap& capacity;
83 typedef typename Graph::template NodeMap<Length> PotentialMap;
84 PotentialMap potential;
92 typedef typename Graph::template NodeMap<Length> NodeMap;
94 const LengthMap &length;
97 typedef typename LengthMap::Key Key;
98 typedef typename LengthMap::Value Value;
100 ModLengthMap(const ResGW& _g,
101 const LengthMap &_length, const NodeMap &_pot) :
102 g(_g), /*rev(_rev),*/ length(_length), pot(_pot) { }
104 Value operator[](typename ResGW::Edge e) const {
106 return length[e]-(pot[g.target(e)]-pot[g.source(e)]);
108 return -length[e]-(pot[g.target(e)]-pot[g.source(e)]);
114 ModLengthMap mod_length;
115 Dijkstra<ResGW, ModLengthMap> dijkstra;
119 /*! \brief The constructor of the class.
121 \param _g The directed graph the algorithm runs on.
122 \param _length The length (weight or cost) of the edges.
123 \param _cap The capacity of the edges.
124 \param _s Source node.
125 \param _t Target node.
127 MinCostFlow(Graph& _g, LengthMap& _length, CapacityMap& _cap,
129 g(_g), length(_length), capacity(_cap), flow(_g), potential(_g),
131 res_graph(g, capacity, flow),
132 mod_length(res_graph, length, potential),
133 dijkstra(res_graph, mod_length) {
137 /*! Tries to augment the flow between s and t by 1.
138 The return value shows if the augmentation is successful.
142 if (!dijkstra.reached(t)) {
144 //Unsuccessful augmentation.
148 //We have to change the potential
149 for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n)
150 potential.set(n, potential[n]+dijkstra.distMap()[n]);
152 //Augmenting on the sortest path
156 e = dijkstra.pred(n);
157 n = dijkstra.predNode(n);
158 res_graph.augment(e,1);
159 //Let's update the total length
160 if (res_graph.forward(e))
161 total_length += length[e];
163 total_length -= length[e];
170 /*! \brief Runs the algorithm.
173 Returns k if there is a flow of value at least k from s to t.
174 Otherwise it returns the maximum value of a flow from s to t.
176 \param k The value of the flow we are looking for.
178 \todo May be it does make sense to be able to start with a nonzero
179 feasible primal-dual solution pair as well.
181 \todo If the actual flow value is bigger than k, then everything is
182 cleared and the algorithm starts from zero flow. Is it a good approach?
185 if (flowValue()>k) reset();
186 while (flowValue()<k && augment()) { }
190 /*! \brief The class is reset to zero flow and potential.
191 The class is reset to zero flow and potential.
195 for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);
196 for (typename Graph::NodeIt n(g); n!=INVALID; ++n) potential.set(n, 0);
199 /*! Returns the value of the actual flow.
201 int flowValue() const {
203 for (typename Graph::OutEdgeIt e(g, s); e!=INVALID; ++e) i+=flow[e];
204 for (typename Graph::InEdgeIt e(g, s); e!=INVALID; ++e) i-=flow[e];
208 /// Total weight of the found flow.
210 /// This function gives back the total weight of the found flow.
211 Length totalLength(){
215 ///Returns a const reference to the EdgeMap \c flow.
217 ///Returns a const reference to the EdgeMap \c flow.
218 const EdgeIntMap &getFlow() const { return flow;}
220 /*! \brief Returns a const reference to the NodeMap \c potential (the dual solution).
222 Returns a const reference to the NodeMap \c potential (the dual solution).
224 const PotentialMap &getPotential() const { return potential;}
226 /*! \brief Checking the complementary slackness optimality criteria.
228 This function checks, whether the given flow and potential
229 satisfiy the complementary slackness cnditions (i.e. these are optimal).
230 This function only checks optimality, doesn't bother with feasibility.
233 bool checkComplementarySlackness(){
236 for(typename Graph::EdgeIt e(g); e!=INVALID; ++e) {
238 mod_pot = length[e]-potential[g.target(e)]+potential[g.source(e)];
240 if (0<fl_e && fl_e<capacity[e]) {
241 /// \todo better comparison is needed for real types, moreover,
242 /// this comparison here is superfluous.
247 if (mod_pot > 0 && fl_e != 0)
249 if (mod_pot < 0 && fl_e != capacity[e])
256 }; //class MinCostFlow
262 #endif //LEMON_MIN_COST_FLOW_H