src/hugo/mincostflows.h
author alpar
Mon, 13 Sep 2004 11:24:35 +0000
changeset 835 eb9587f09b42
parent 785 a9b0863c2265
child 860 3577b3db6089
permissions -rw-r--r--
Remove one remaining range checking.
     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 
    15 namespace 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