COIN-OR::LEMON - Graph Library

source: lemon-0.x/src/hugo/mincostflows.h @ 788:c3187cafcabf

Last change on this file since 788:c3187cafcabf was 788:c3187cafcabf, checked in by marci, 15 years ago

mincostflow_test is ok.

File size: 6.0 KB
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1// -*- c++ -*-
2#ifndef HUGO_MINCOSTFLOWS_H
3#define HUGO_MINCOSTFLOWS_H
4
5///\ingroup flowalgs
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
15namespace hugo {
16
17/// \addtogroup flowalgs
18/// @{
19
20  ///\brief Implementation of an algorithm for finding a flow of value \c k
21  ///(for small values of \c k) having minimal total cost between 2 nodes
22  ///
23  ///
24  /// The class \ref hugo::MinCostFlows "MinCostFlows" implements
25  /// an algorithm for finding a flow of value \c k
26  ///(for small values of \c k) having minimal total cost 
27  /// from a given source node to a given target node in an
28  /// edge-weighted directed graph having nonnegative integer capacities.
29  /// The range of the length (weight) function is nonnegative reals but
30  /// the range of capacity function is the set of nonnegative integers.
31  /// It is not a polinomial time algorithm for counting the minimum cost
32  /// maximal flow, since it counts the minimum cost flow for every value 0..M
33  /// where \c M is the value of the maximal flow.
34  ///
35  ///\author Attila Bernath
36  template <typename Graph, typename LengthMap, typename CapacityMap>
37  class MinCostFlows {
38
39    typedef typename LengthMap::ValueType Length;
40
41    //Warning: this should be integer type
42    typedef typename CapacityMap::ValueType Capacity;
43   
44    typedef typename Graph::Node Node;
45    typedef typename Graph::NodeIt NodeIt;
46    typedef typename Graph::Edge Edge;
47    typedef typename Graph::OutEdgeIt OutEdgeIt;
48    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
49
50    //    typedef ConstMap<Edge,int> ConstMap;
51
52    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
53    typedef typename ResGraphType::Edge ResGraphEdge;
54
55    class ModLengthMap {   
56      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
57      typedef typename Graph::template NodeMap<Length> NodeMap;
58      const ResGraphType& G;
59      //      const EdgeIntMap& rev;
60      const LengthMap &ol;
61      const NodeMap &pot;
62    public :
63      typedef typename LengthMap::KeyType KeyType;
64      typedef typename LengthMap::ValueType ValueType;
65       
66      ValueType operator[](typename ResGraphType::Edge e) const {     
67        if (G.forward(e))
68          return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
69        else
70          return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
71      }     
72       
73      ModLengthMap(const ResGraphType& _G,
74                   const LengthMap &o,  const NodeMap &p) :
75        G(_G), /*rev(_rev),*/ ol(o), pot(p){};
76    };//ModLengthMap
77
78
79  protected:
80   
81    //Input
82    const Graph& G;
83    const LengthMap& length;
84    const CapacityMap& capacity;
85
86
87    //auxiliary variables
88
89    //To store the flow
90    EdgeIntMap flow;
91    //To store the potential (dual variables)
92    typedef typename Graph::template NodeMap<Length> PotentialMap;
93    PotentialMap potential;
94   
95
96    Length total_length;
97
98
99  public :
100
101
102    MinCostFlows(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G),
103      length(_length), capacity(_cap), flow(_G), potential(_G){ }
104
105   
106    ///Runs the algorithm.
107
108    ///Runs the algorithm.
109    ///Returns k if there are at least k edge-disjoint paths from s to t.
110    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
111    ///\todo May be it does make sense to be able to start with a nonzero
112    /// feasible primal-dual solution pair as well.
113    int run(Node s, Node t, int k) {
114
115      //Resetting variables from previous runs
116      total_length = 0;
117     
118      for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0);
119
120      //Initialize the potential to zero
121      for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0);
122     
123     
124      //We need a residual graph
125      ResGraphType res_graph(G, capacity, flow);
126
127
128      ModLengthMap mod_length(res_graph, length, potential);
129
130      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
131
132      int i;
133      for (i=0; i<k; ++i){
134        dijkstra.run(s);
135        if (!dijkstra.reached(t)){
136          //There are no k paths from s to t
137          break;
138        };
139       
140        //We have to change the potential
141        for(typename ResGraphType::NodeIt n(res_graph); n!=INVALID; ++n)
142          potential[n] += dijkstra.distMap()[n];
143
144
145        //Augmenting on the sortest path
146        Node n=t;
147        ResGraphEdge e;
148        while (n!=s){
149          e = dijkstra.pred(n);
150          n = dijkstra.predNode(n);
151          res_graph.augment(e,1);
152          //Let's update the total length
153          if (res_graph.forward(e))
154            total_length += length[e];
155          else
156            total_length -= length[e];     
157        }
158
159         
160      }
161     
162
163      return i;
164    }
165
166
167
168
169    ///This function gives back the total length of the found paths.
170    ///Assumes that \c run() has been run and nothing changed since then.
171    Length totalLength(){
172      return total_length;
173    }
174
175    ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must
176    ///be called before using this function.
177    const EdgeIntMap &getFlow() const { return flow;}
178
179  ///Returns a const reference to the NodeMap \c potential (the dual solution).
180    /// \pre \ref run() must be called before using this function.
181    const PotentialMap &getPotential() const { return potential;}
182
183    ///This function checks, whether the given solution is optimal
184    ///Running after a \c run() should return with true
185    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
186    ///
187    ///\todo Is this OK here?
188    bool checkComplementarySlackness(){
189      Length mod_pot;
190      Length fl_e;
191        for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) {
192        //C^{\Pi}_{i,j}
193        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
194        fl_e = flow[e];
195        //      std::cout << fl_e << std::endl;
196        if (0<fl_e && fl_e<capacity[e]){
197          if (mod_pot != 0)
198            return false;
199        }
200        else{
201          if (mod_pot > 0 && fl_e != 0)
202            return false;
203          if (mod_pot < 0 && fl_e != capacity[e])
204            return false;
205        }
206      }
207      return true;
208    }
209   
210
211  }; //class MinCostFlows
212
213  ///@}
214
215} //namespace hugo
216
217#endif //HUGO_MINCOSTFLOWS_H
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