COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/work/athos/mincostflow.h @ 633:305bd9c56f10

Last change on this file since 633:305bd9c56f10 was 633:305bd9c56f10, checked in by athos, 17 years ago

Slight modifications.

File size: 6.3 KB
Line 
1// -*- c++ -*-
2#ifndef HUGO_MINCOSTFLOW_H
3#define HUGO_MINCOSTFLOW_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 <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::MinCostFlow "MinCostFlow" implements
26  /// an algorithm for solving the following general minimum cost flow problem>
27  ///
28  ///
29  ///
30  /// \warning It is assumed here that the problem has a feasible solution
31  ///
32  /// The range of the length (weight) function is nonnegative reals but
33  /// the range of capacity function is the set of nonnegative integers.
34  /// It is not a polinomial time algorithm for counting the minimum cost
35  /// maximal flow, since it counts the minimum cost flow for every value 0..M
36  /// where \c M is the value of the maximal flow.
37  ///
38  ///\author Attila Bernath
39  template <typename Graph, typename LengthMap, typename SupplyMap>
40  class MinCostFlow {
41
42    typedef typename LengthMap::ValueType Length;
43
44
45    typedef typename SupplyMap::ValueType Supply;
46   
47    typedef typename Graph::Node Node;
48    typedef typename Graph::NodeIt NodeIt;
49    typedef typename Graph::Edge Edge;
50    typedef typename Graph::OutEdgeIt OutEdgeIt;
51    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
52
53    //    typedef ConstMap<Edge,int> ConstMap;
54
55    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
56    typedef typename ResGraphType::Edge ResGraphEdge;
57
58    class ModLengthMap {   
59      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
60      typedef typename Graph::template NodeMap<Length> NodeMap;
61      const ResGraphType& G;
62      //      const EdgeIntMap& rev;
63      const LengthMap &ol;
64      const NodeMap &pot;
65    public :
66      typedef typename LengthMap::KeyType KeyType;
67      typedef typename LengthMap::ValueType ValueType;
68       
69      ValueType operator[](typename ResGraphType::Edge e) const {     
70        if (G.forward(e))
71          return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
72        else
73          return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
74      }     
75       
76      ModLengthMap(const ResGraphType& _G,
77                   const LengthMap &o,  const NodeMap &p) :
78        G(_G), /*rev(_rev),*/ ol(o), pot(p){};
79    };//ModLengthMap
80
81
82  protected:
83   
84    //Input
85    const Graph& G;
86    const LengthMap& length;
87    const SupplyMap& supply;//supply or demand of nodes
88
89
90    //auxiliary variables
91
92    //To store the flow
93    EdgeIntMap flow;
94    //To store the potentila (dual variables)
95    typename Graph::template NodeMap<Length> potential;
96    //To store excess-deficit values
97    SupplyMap excess;
98   
99
100    Length total_length;
101
102
103  public :
104
105
106    MinCostFlow(Graph& _G, LengthMap& _length, SupplyMap& _supply) : G(_G),
107      length(_length), supply(_supply), flow(_G), potential(_G){ }
108
109   
110    ///Runs the algorithm.
111
112    ///Runs the algorithm.
113    ///Returns k if there are at least k edge-disjoint paths from s to t.
114    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
115    ///\todo May be it does make sense to be able to start with a nonzero
116    /// feasible primal-dual solution pair as well.
117    int run() {
118
119      //Resetting variables from previous runs
120      total_length = 0;
121     
122      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
123        flow.set(e,0);
124      }
125
126      //Initial value for delta
127      Supply delta = 0;
128     
129      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
130        if (delta < abs(supply[e])){
131          delta = abs(supply[e]);
132        }
133        excess.set(n,supply[e]);
134        //Initialize the copy of the Dijkstra potential to zero
135        potential.set(n,0);
136      }
137     
138
139     
140      //We need a residual graph which is uncapacitated
141      ResGraphType res_graph(G, flow);
142
143
144     
145      ModLengthMap mod_length(res_graph, length, potential);
146
147      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
148
149
150      int i;
151      for (i=0; i<k; ++i){
152        dijkstra.run(s);
153        if (!dijkstra.reached(t)){
154          //There are no k paths from s to t
155          break;
156        };
157       
158        //We have to copy the potential
159        FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){
160          potential[n] += dijkstra.distMap()[n];
161        }
162
163        /*
164        {
165
166          typename ResGraphType::NodeIt n;
167          for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {
168              potential[n] += dijkstra.distMap()[n];
169          }
170        }
171        */
172
173        //Augmenting on the sortest path
174        Node n=t;
175        ResGraphEdge e;
176        while (n!=s){
177          e = dijkstra.pred(n);
178          n = dijkstra.predNode(n);
179          res_graph.augment(e,delta);
180          //Let's update the total length
181          if (res_graph.forward(e))
182            total_length += length[e];
183          else
184            total_length -= length[e];     
185        }
186
187         
188      }
189     
190
191      return i;
192    }
193
194
195
196
197    ///This function gives back the total length of the found paths.
198    ///Assumes that \c run() has been run and nothing changed since then.
199    Length totalLength(){
200      return total_length;
201    }
202
203    ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
204    ///be called before using this function.
205    const EdgeIntMap &getFlow() const { return flow;}
206
207  ///Returns a const reference to the NodeMap \c potential (the dual solution).
208    /// \pre \ref run() must be called before using this function.
209    const EdgeIntMap &getPotential() const { return potential;}
210
211    ///This function checks, whether the given solution is optimal
212    ///Running after a \c run() should return with true
213    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
214    ///
215    ///\todo Is this OK here?
216    bool checkComplementarySlackness(){
217      Length mod_pot;
218      Length fl_e;
219      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
220        //C^{\Pi}_{i,j}
221        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
222        fl_e = flow[e];
223        //      std::cout << fl_e << std::endl;
224        if (0<fl_e && fl_e<capacity[e]){
225          if (mod_pot != 0)
226            return false;
227        }
228        else{
229          if (mod_pot > 0 && fl_e != 0)
230            return false;
231          if (mod_pot < 0 && fl_e != capacity[e])
232            return false;
233        }
234      }
235      return true;
236    }
237   
238
239  }; //class MinCostFlow
240
241  ///@}
242
243} //namespace hugo
244
245#endif //HUGO_MINCOSTFLOW_H
Note: See TracBrowser for help on using the repository browser.