1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
9 | * Permission to use, modify and distribute this software is granted |
---|
10 | * provided that this copyright notice appears in all copies. For |
---|
11 | * precise terms see the accompanying LICENSE file. |
---|
12 | * |
---|
13 | * This software is provided "AS IS" with no warranty of any kind, |
---|
14 | * express or implied, and with no claim as to its suitability for any |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_MIN_COST_MAX_FLOW_H |
---|
20 | #define LEMON_MIN_COST_MAX_FLOW_H |
---|
21 | |
---|
22 | /// \ingroup min_cost_flow |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief An efficient algorithm for finding a minimum cost maximum flow. |
---|
26 | |
---|
27 | #include <lemon/preflow.h> |
---|
28 | #include <lemon/network_simplex.h> |
---|
29 | #include <lemon/maps.h> |
---|
30 | |
---|
31 | namespace lemon { |
---|
32 | |
---|
33 | /// \addtogroup min_cost_flow |
---|
34 | /// @{ |
---|
35 | |
---|
36 | /// \brief An efficient algorithm for finding a minimum cost |
---|
37 | /// maximum flow. |
---|
38 | /// |
---|
39 | /// \ref MinCostMaxFlow implements an efficient algorithm for |
---|
40 | /// finding a maximum flow having minimal total cost from a given |
---|
41 | /// source node to a given target node in a directed graph. |
---|
42 | /// |
---|
43 | /// \ref MinCostMaxFlow uses \ref Preflow for finding the maximum |
---|
44 | /// flow value and \ref NetworkSimplex for finding a minimum cost |
---|
45 | /// flow of that value. |
---|
46 | /// According to our benchmark tests \ref Preflow is generally the |
---|
47 | /// most efficient algorithm for the maximum flow problem and |
---|
48 | /// \ref NetworkSimplex is the most efficient for the minimum cost |
---|
49 | /// flow problem in LEMON. |
---|
50 | /// |
---|
51 | /// \tparam Graph The directed graph type the algorithm runs on. |
---|
52 | /// \tparam CapacityMap The type of the capacity (upper bound) map. |
---|
53 | /// \tparam CostMap The type of the cost (length) map. |
---|
54 | /// |
---|
55 | /// \warning |
---|
56 | /// - Edge capacities and costs should be \e non-negative \e integers. |
---|
57 | /// However \c CostMap::Value must be signed type. |
---|
58 | /// - \c CapacityMap::Value must be convertible to \c CostMap::Value. |
---|
59 | /// |
---|
60 | /// \author Peter Kovacs |
---|
61 | |
---|
62 | template < typename Graph, |
---|
63 | typename CapacityMap = typename Graph::template EdgeMap<int>, |
---|
64 | typename CostMap = typename Graph::template EdgeMap<int> > |
---|
65 | class MinCostMaxFlow |
---|
66 | { |
---|
67 | typedef typename Graph::Node Node; |
---|
68 | typedef typename Graph::Edge Edge; |
---|
69 | |
---|
70 | typedef typename CapacityMap::Value Capacity; |
---|
71 | typedef typename CostMap::Value Cost; |
---|
72 | typedef typename Graph::template NodeMap<Cost> SupplyMap; |
---|
73 | |
---|
74 | typedef Preflow<Graph, CapacityMap> MaxFlowImpl; |
---|
75 | typedef NetworkSimplex< Graph, CapacityMap, CapacityMap, |
---|
76 | CostMap, SupplyMap > MinCostFlowImpl; |
---|
77 | |
---|
78 | public: |
---|
79 | |
---|
80 | /// The type of the flow map. |
---|
81 | typedef typename Graph::template EdgeMap<Capacity> FlowMap; |
---|
82 | /// The type of the potential map. |
---|
83 | typedef typename Graph::template NodeMap<Cost> PotentialMap; |
---|
84 | |
---|
85 | private: |
---|
86 | |
---|
87 | // The directed graph the algorithm runs on |
---|
88 | const Graph &_graph; |
---|
89 | // The modified capacity map |
---|
90 | const CapacityMap &_capacity; |
---|
91 | // The cost map |
---|
92 | const CostMap &_cost; |
---|
93 | |
---|
94 | // Edge map of the found flow |
---|
95 | FlowMap _flow; |
---|
96 | // Node map of the found potentials |
---|
97 | PotentialMap _potential; |
---|
98 | |
---|
99 | // The source node |
---|
100 | Node _source; |
---|
101 | // The target node |
---|
102 | Node _target; |
---|
103 | |
---|
104 | public: |
---|
105 | |
---|
106 | /// \brief The constructor of the class. |
---|
107 | /// |
---|
108 | /// The constructor of the class. |
---|
109 | /// |
---|
110 | /// \param _graph The directed graph the algorithm runs on. |
---|
111 | /// \param _capacity The capacities (upper bounds) of the edges. |
---|
112 | /// \param _cost The cost (length) values of the edges. |
---|
113 | /// \param _s The source node. |
---|
114 | /// \param _t The target node. |
---|
115 | MinCostMaxFlow( const Graph &graph, |
---|
116 | const CapacityMap &capacity, |
---|
117 | const CostMap &cost, |
---|
118 | Node s, Node t ) : |
---|
119 | _graph(graph), _capacity(capacity), _cost(cost), _flow(graph), |
---|
120 | _potential(graph), _source(s), _target(t) |
---|
121 | {} |
---|
122 | |
---|
123 | /// \brief Runs the algorithm. |
---|
124 | /// |
---|
125 | /// Runs the algorithm. |
---|
126 | void run() { |
---|
127 | MaxFlowImpl preflow(_graph, _capacity, _source, _target); |
---|
128 | preflow.flowMap(_flow).runMinCut(); |
---|
129 | MinCostFlowImpl mcf( _graph, _capacity, _cost, |
---|
130 | _source, _target, preflow.flowValue() ); |
---|
131 | mcf.run(); |
---|
132 | _flow = mcf.flowMap(); |
---|
133 | _potential = mcf.potentialMap(); |
---|
134 | } |
---|
135 | |
---|
136 | /// \brief Returns a const reference to the edge map storing the |
---|
137 | /// found flow. |
---|
138 | /// |
---|
139 | /// Returns a const reference to the edge map storing the found flow. |
---|
140 | /// |
---|
141 | /// \pre \ref run() must be called before using this function. |
---|
142 | const FlowMap& flowMap() const { |
---|
143 | return _flow; |
---|
144 | } |
---|
145 | |
---|
146 | /// \brief Returns a const reference to the node map storing the |
---|
147 | /// found potentials (the dual solution). |
---|
148 | /// |
---|
149 | /// Returns a const reference to the node map storing the found |
---|
150 | /// potentials (the dual solution). |
---|
151 | /// |
---|
152 | /// \pre \ref run() must be called before using this function. |
---|
153 | const PotentialMap& potentialMap() const { |
---|
154 | return _potential; |
---|
155 | } |
---|
156 | |
---|
157 | /// \brief Returns the total cost of the found flow. |
---|
158 | /// |
---|
159 | /// Returns the total cost of the found flow. The complexity of the |
---|
160 | /// function is \f$ O(e) \f$. |
---|
161 | /// |
---|
162 | /// \pre \ref run() must be called before using this function. |
---|
163 | Cost totalCost() const { |
---|
164 | Cost c = 0; |
---|
165 | for (typename Graph::EdgeIt e(_graph); e != INVALID; ++e) |
---|
166 | c += _flow[e] * _cost[e]; |
---|
167 | return c; |
---|
168 | } |
---|
169 | |
---|
170 | }; //class MinCostMaxFlow |
---|
171 | |
---|
172 | ///@} |
---|
173 | |
---|
174 | } //namespace lemon |
---|
175 | |
---|
176 | #endif //LEMON_MIN_COST_MAX_FLOW_H |
---|