COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/mincostflows.h @ 554:2d27cbaa982d

Last change on this file since 554:2d27cbaa982d was 554:2d27cbaa982d, checked in by athos, 16 years ago

Method checkSolution() added.

File size: 6.4 KB
Line 
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#include <iostream>
10#include <hugo/dijkstra.h>
11#include <graph_wrapper.h>
12#include <hugo/maps.h>
13#include <vector>
14#include <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   
81    //Input
82    const Graph& G;
83    const LengthMap& length;
84    const CapacityMap& capacity;
85
86    //auxiliary variables
87
88    //To store the flow
89    EdgeIntMap flow;
90    //To store the potentila (dual variables)
91    typename Graph::template NodeMap<Length> potential;
92   
93    //Container to store found paths
94    //std::vector< std::vector<Edge> > paths;
95    //typedef DirPath<Graph> DPath;
96    //DPath paths;
97
98
99    Length total_length;
100
101  public :
102
103
104    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
105      length(_length), capacity(_cap), flow(_G), potential(_G){ }
106
107   
108    ///Runs the algorithm.
109
110    ///Runs the algorithm.
111    ///Returns k if there are at least k edge-disjoint paths from s to t.
112    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
113    int run(Node s, Node t, int k) {
114
115      //Resetting variables from previous runs
116      total_length = 0;
117     
118      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
119        flow.set(e,0);
120      }
121     
122      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
123        //cout << potential[n]<<endl;
124        potential.set(n,0);
125      }
126     
127
128     
129      //We need a residual graph
130      ResGraphType res_graph(G, capacity, flow);
131
132      //Initialize the copy of the Dijkstra potential to zero
133     
134      //typename ResGraphType::template NodeMap<Length> potential(res_graph);
135
136
137      ModLengthMap mod_length(res_graph, length, potential);
138
139      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
140
141      int i;
142      for (i=0; i<k; ++i){
143        dijkstra.run(s);
144        if (!dijkstra.reached(t)){
145          //There are no k paths from s to t
146          break;
147        };
148       
149        {
150          //We have to copy the potential
151          typename ResGraphType::NodeIt n;
152          for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
153              potential[n] += dijkstra.distMap()[n];
154          }
155        }
156
157
158        //Augmenting on the sortest path
159        Node n=t;
160        ResGraphEdge e;
161        while (n!=s){
162          e = dijkstra.pred(n);
163          n = dijkstra.predNode(n);
164          res_graph.augment(e,1);
165          //Let's update the total length
166          if (res_graph.forward(e))
167            total_length += length[e];
168          else
169            total_length -= length[e];     
170        }
171
172         
173      }
174     
175
176      return i;
177    }
178
179
180
181
182    ///This function gives back the total length of the found paths.
183    ///Assumes that \c run() has been run and nothing changed since then.
184    Length totalLength(){
185      return total_length;
186    }
187
188    //This function checks, whether the given solution is optimal
189    //Running after a \c run() should return with true
190    //In this "state of the art" this only check optimality, doesn't bother with feasibility
191    bool checkSolution(){
192      Length mod_pot;
193      Length fl_e;
194      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
195        //C^{\Pi}_{i,j}
196        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
197        fl_e = flow[e];
198        //      std::cout << fl_e << std::endl;
199        if (0<fl_e && fl_e<capacity[e]){
200          if (mod_pot != 0)
201            return false;
202        }
203        else{
204          if (mod_pot > 0 && fl_e != 0)
205            return false;
206          if (mod_pot < 0 && fl_e != capacity[e])
207            return false;
208        }
209      }
210      return true;
211    }
212   
213    /*
214      ///\todo To be implemented later
215
216    ///This function gives back the \c j-th path in argument p.
217    ///Assumes that \c run() has been run and nothing changed since then.
218    /// \warning It is assumed that \c p is constructed to be a path of graph \c G. If \c j is greater than the result of previous \c run, then the result here will be an empty path.
219    template<typename DirPath>
220    void getPath(DirPath& p, int j){
221      p.clear();
222      typename DirPath::Builder B(p);
223      for(typename std::vector<Edge>::iterator i=paths[j].begin();
224          i!=paths[j].end(); ++i ){
225        B.pushBack(*i);
226      }
227
228      B.commit();
229    }
230
231    */
232
233  }; //class MinCostFlows
234
235  ///@}
236
237} //namespace hugo
238
239#endif //HUGO_MINCOSTFLOW_H
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