COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/mincostflows.h @ 696:48aa9ace1d7d

Last change on this file since 696:48aa9ace1d7d was 661:d306e777117e, checked in by athos, 17 years ago

Corrected some obvious errors.

File size: 6.0 KB
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1// -*- c++ -*-
2#ifndef HUGO_MINCOSTFLOWS_H
3#define HUGO_MINCOSTFLOWS_H
4
5///\ingroup galgs
6///\file
7///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost
8
9
10#include <hugo/dijkstra.h>
11#include <hugo/graph_wrapper.h>
12#include <hugo/maps.h>
13#include <vector>
14#include <hugo/for_each_macros.h>
15
16namespace hugo {
17
18/// \addtogroup galgs
19/// @{
20
21  ///\brief Implementation of an algorithm for finding a flow of value \c k
22  ///(for small values of \c k) having minimal total cost between 2 nodes
23  ///
24  ///
25  /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
26  /// an algorithm for finding a flow of value \c k
27  ///(for small values of \c k) having minimal total cost 
28  /// from a given source node to a given target node in an
29  /// edge-weighted directed graph having nonnegative integer capacities.
30  /// The range of the length (weight) function is nonnegative reals but
31  /// the range of capacity function is the set of nonnegative integers.
32  /// It is not a polinomial time algorithm for counting the minimum cost
33  /// maximal flow, since it counts the minimum cost flow for every value 0..M
34  /// where \c M is the value of the maximal flow.
35  ///
36  ///\author Attila Bernath
37  template <typename Graph, typename LengthMap, typename CapacityMap>
38  class MinCostFlows {
39
40    typedef typename LengthMap::ValueType Length;
41
42    //Warning: this should be integer type
43    typedef typename CapacityMap::ValueType Capacity;
44   
45    typedef typename Graph::Node Node;
46    typedef typename Graph::NodeIt NodeIt;
47    typedef typename Graph::Edge Edge;
48    typedef typename Graph::OutEdgeIt OutEdgeIt;
49    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
50
51    //    typedef ConstMap<Edge,int> ConstMap;
52
53    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
54    typedef typename ResGraphType::Edge ResGraphEdge;
55
56    class ModLengthMap {   
57      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
58      typedef typename Graph::template NodeMap<Length> NodeMap;
59      const ResGraphType& G;
60      //      const EdgeIntMap& rev;
61      const LengthMap &ol;
62      const NodeMap &pot;
63    public :
64      typedef typename LengthMap::KeyType KeyType;
65      typedef typename LengthMap::ValueType ValueType;
66       
67      ValueType operator[](typename ResGraphType::Edge e) const {     
68        if (G.forward(e))
69          return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
70        else
71          return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
72      }     
73       
74      ModLengthMap(const ResGraphType& _G,
75                   const LengthMap &o,  const NodeMap &p) :
76        G(_G), /*rev(_rev),*/ ol(o), pot(p){};
77    };//ModLengthMap
78
79
80  protected:
81   
82    //Input
83    const Graph& G;
84    const LengthMap& length;
85    const CapacityMap& capacity;
86
87
88    //auxiliary variables
89
90    //To store the flow
91    EdgeIntMap flow;
92    //To store the potentila (dual variables)
93    typedef typename Graph::template NodeMap<Length> PotentialMap;
94    PotentialMap potential;
95   
96
97    Length total_length;
98
99
100  public :
101
102
103    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
104      length(_length), capacity(_cap), flow(_G), potential(_G){ }
105
106   
107    ///Runs the algorithm.
108
109    ///Runs the algorithm.
110    ///Returns k if there are at least k edge-disjoint paths from s to t.
111    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
112    ///\todo May be it does make sense to be able to start with a nonzero
113    /// feasible primal-dual solution pair as well.
114    int run(Node s, Node t, int k) {
115
116      //Resetting variables from previous runs
117      total_length = 0;
118     
119      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
120        flow.set(e,0);
121      }
122
123      //Initialize the potential to zero
124      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
125        potential.set(n,0);
126      }
127     
128
129     
130      //We need a residual graph
131      ResGraphType res_graph(G, capacity, flow);
132
133
134      ModLengthMap mod_length(res_graph, length, potential);
135
136      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
137
138      int i;
139      for (i=0; i<k; ++i){
140        dijkstra.run(s);
141        if (!dijkstra.reached(t)){
142          //There are no k paths from s to t
143          break;
144        };
145       
146        //We have to change the potential
147        FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){
148          potential[n] += dijkstra.distMap()[n];
149        }
150
151
152        //Augmenting on the sortest path
153        Node n=t;
154        ResGraphEdge e;
155        while (n!=s){
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];
162          else
163            total_length -= length[e];     
164        }
165
166         
167      }
168     
169
170      return i;
171    }
172
173
174
175
176    ///This function gives back the total length of the found paths.
177    ///Assumes that \c run() has been run and nothing changed since then.
178    Length totalLength(){
179      return total_length;
180    }
181
182    ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
183    ///be called before using this function.
184    const EdgeIntMap &getFlow() const { return flow;}
185
186  ///Returns a const reference to the NodeMap \c potential (the dual solution).
187    /// \pre \ref run() must be called before using this function.
188    const PotentialMap &getPotential() const { return potential;}
189
190    ///This function checks, whether the given solution is optimal
191    ///Running after a \c run() should return with true
192    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
193    ///
194    ///\todo Is this OK here?
195    bool checkComplementarySlackness(){
196      Length mod_pot;
197      Length fl_e;
198      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
199        //C^{\Pi}_{i,j}
200        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
201        fl_e = flow[e];
202        //      std::cout << fl_e << std::endl;
203        if (0<fl_e && fl_e<capacity[e]){
204          if (mod_pot != 0)
205            return false;
206        }
207        else{
208          if (mod_pot > 0 && fl_e != 0)
209            return false;
210          if (mod_pot < 0 && fl_e != capacity[e])
211            return false;
212        }
213      }
214      return true;
215    }
216   
217
218  }; //class MinCostFlows
219
220  ///@}
221
222} //namespace hugo
223
224#endif //HUGO_MINCOSTFLOWS_H
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