alpar@906: /* -*- C++ -*-
alpar@921:  * src/lemon/min_cost_flow.h - Part of LEMON, a generic C++ optimization library
alpar@906:  *
alpar@906:  * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@906:  * (Egervary Combinatorial Optimization Research Group, EGRES).
alpar@906:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
alpar@906:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
alpar@906:  *
alpar@906:  */
alpar@906: 
alpar@921: #ifndef LEMON_MIN_COST_FLOW_H
alpar@921: #define LEMON_MIN_COST_FLOW_H
alpar@899: 
alpar@899: ///\ingroup flowalgs
alpar@899: ///\file
alpar@899: ///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost 
alpar@899: 
alpar@899: 
alpar@921: #include <lemon/dijkstra.h>
alpar@921: #include <lemon/graph_wrapper.h>
alpar@921: #include <lemon/maps.h>
alpar@899: #include <vector>
alpar@899: 
alpar@921: namespace lemon {
alpar@899: 
alpar@899: /// \addtogroup flowalgs
alpar@899: /// @{
alpar@899: 
alpar@899:   ///\brief Implementation of an algorithm for finding a flow of value \c k 
alpar@899:   ///(for small values of \c k) having minimal total cost between 2 nodes 
alpar@899:   /// 
alpar@899:   ///
alpar@921:   /// The class \ref lemon::MinCostFlow "MinCostFlow" implements
alpar@899:   /// an algorithm for finding a flow of value \c k 
alpar@899:   /// having minimal total cost 
alpar@899:   /// from a given source node to a given target node in an
alpar@899:   /// edge-weighted directed graph. To this end, 
alpar@899:   /// the edge-capacities and edge-weitghs have to be nonnegative. 
alpar@899:   /// The edge-capacities should be integers, but the edge-weights can be 
alpar@899:   /// integers, reals or of other comparable numeric type.
alpar@899:   /// This algorithm is intended to use only for small values of \c k, 
alpar@899:   /// since it is only polynomial in k, 
alpar@899:   /// not in the length of k (which is log k). 
alpar@899:   /// In order to find the minimum cost flow of value \c k it 
alpar@899:   /// finds the minimum cost flow of value \c i for every 
alpar@899:   /// \c i between 0 and \c k. 
alpar@899:   ///
alpar@899:   ///\param Graph The directed graph type the algorithm runs on.
alpar@899:   ///\param LengthMap The type of the length map.
alpar@899:   ///\param CapacityMap The capacity map type.
alpar@899:   ///
alpar@899:   ///\author Attila Bernath
alpar@899:   template <typename Graph, typename LengthMap, typename CapacityMap>
alpar@899:   class MinCostFlow {
alpar@899: 
alpar@899:     typedef typename LengthMap::ValueType Length;
alpar@899: 
alpar@899:     //Warning: this should be integer type
alpar@899:     typedef typename CapacityMap::ValueType Capacity;
alpar@899:     
alpar@899:     typedef typename Graph::Node Node;
alpar@899:     typedef typename Graph::NodeIt NodeIt;
alpar@899:     typedef typename Graph::Edge Edge;
alpar@899:     typedef typename Graph::OutEdgeIt OutEdgeIt;
alpar@899:     typedef typename Graph::template EdgeMap<int> EdgeIntMap;
alpar@899: 
alpar@899: 
marci@910:     typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGW;
marci@910:     typedef typename ResGW::Edge ResGraphEdge;
alpar@899: 
alpar@899:     class ModLengthMap {   
alpar@899:       typedef typename Graph::template NodeMap<Length> NodeMap;
marci@910:       const ResGW& G;
alpar@899:       const LengthMap &ol;
alpar@899:       const NodeMap &pot;
alpar@899:     public :
alpar@899:       typedef typename LengthMap::KeyType KeyType;
alpar@899:       typedef typename LengthMap::ValueType ValueType;
alpar@899: 	
marci@910:       ValueType operator[](typename ResGW::Edge e) const {     
alpar@899: 	if (G.forward(e))
alpar@899: 	  return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
alpar@899: 	else
alpar@899: 	  return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
alpar@899:       }     
alpar@899: 	
marci@910:       ModLengthMap(const ResGW& _G,
alpar@899: 		   const LengthMap &o,  const NodeMap &p) : 
alpar@899: 	G(_G), /*rev(_rev),*/ ol(o), pot(p){}; 
alpar@899:     };//ModLengthMap
alpar@899: 
alpar@899: 
alpar@899:   protected:
alpar@899:     
alpar@899:     //Input
alpar@899:     const Graph& G;
alpar@899:     const LengthMap& length;
alpar@899:     const CapacityMap& capacity;
alpar@899: 
alpar@899: 
alpar@899:     //auxiliary variables
alpar@899: 
alpar@899:     //To store the flow
alpar@899:     EdgeIntMap flow; 
alpar@899:     //To store the potential (dual variables)
alpar@899:     typedef typename Graph::template NodeMap<Length> PotentialMap;
alpar@899:     PotentialMap potential;
alpar@899:     
alpar@899: 
alpar@899:     Length total_length;
alpar@899: 
alpar@899: 
alpar@899:   public :
alpar@899: 
alpar@899:     /// The constructor of the class.
alpar@899:     
alpar@899:     ///\param _G The directed graph the algorithm runs on. 
alpar@899:     ///\param _length The length (weight or cost) of the edges. 
alpar@899:     ///\param _cap The capacity of the edges. 
alpar@899:     MinCostFlow(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), 
alpar@899:       length(_length), capacity(_cap), flow(_G), potential(_G){ }
alpar@899: 
alpar@899:     
alpar@899:     ///Runs the algorithm.
alpar@899:     
alpar@899:     ///Runs the algorithm.
alpar@899:     ///Returns k if there is a flow of value at least k edge-disjoint 
alpar@899:     ///from s to t.
alpar@899:     ///Otherwise it returns the maximum value of a flow from s to t.
alpar@899:     ///
alpar@899:     ///\param s The source node.
alpar@899:     ///\param t The target node.
alpar@899:     ///\param k The value of the flow we are looking for.
alpar@899:     ///
alpar@899:     ///\todo May be it does make sense to be able to start with a nonzero 
alpar@899:     /// feasible primal-dual solution pair as well.
alpar@899:     int run(Node s, Node t, int k) {
alpar@899: 
alpar@899:       //Resetting variables from previous runs
alpar@899:       total_length = 0;
alpar@899:       
alpar@899:       for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0);
alpar@899: 
alpar@899:       //Initialize the potential to zero
alpar@899:       for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0);
alpar@899:       
alpar@899:       
alpar@899:       //We need a residual graph
marci@910:       ResGW res_graph(G, capacity, flow);
alpar@899: 
alpar@899: 
alpar@899:       ModLengthMap mod_length(res_graph, length, potential);
alpar@899: 
marci@910:       Dijkstra<ResGW, ModLengthMap> dijkstra(res_graph, mod_length);
alpar@899: 
alpar@899:       int i;
alpar@899:       for (i=0; i<k; ++i){
alpar@899: 	dijkstra.run(s);
alpar@899: 	if (!dijkstra.reached(t)){
alpar@899: 	  //There are no flow of value k from s to t
alpar@899: 	  break;
alpar@899: 	};
alpar@899: 	
alpar@899: 	//We have to change the potential
marci@910:         for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n)
alpar@899: 	  potential[n] += dijkstra.distMap()[n];
alpar@899: 
alpar@899: 
alpar@899: 	//Augmenting on the sortest path
alpar@899: 	Node n=t;
alpar@899: 	ResGraphEdge e;
alpar@899: 	while (n!=s){
alpar@899: 	  e = dijkstra.pred(n);
alpar@899: 	  n = dijkstra.predNode(n);
alpar@899: 	  res_graph.augment(e,1);
alpar@899: 	  //Let's update the total length
alpar@899: 	  if (res_graph.forward(e))
alpar@899: 	    total_length += length[e];
alpar@899: 	  else 
alpar@899: 	    total_length -= length[e];	    
alpar@899: 	}
alpar@899: 
alpar@899: 	  
alpar@899:       }
alpar@899:       
alpar@899: 
alpar@899:       return i;
alpar@899:     }
alpar@899: 
alpar@899: 
alpar@899: 
alpar@899:     /// Gives back the total weight of the found flow.
alpar@899: 
alpar@899:     ///This function gives back the total weight of the found flow.
alpar@899:     ///Assumes that \c run() has been run and nothing changed since then.
alpar@899:     Length totalLength(){
alpar@899:       return total_length;
alpar@899:     }
alpar@899: 
alpar@899:     ///Returns a const reference to the EdgeMap \c flow. 
alpar@899: 
alpar@899:     ///Returns a const reference to the EdgeMap \c flow. 
alpar@899:     ///\pre \ref run() must
alpar@899:     ///be called before using this function.
alpar@899:     const EdgeIntMap &getFlow() const { return flow;}
alpar@899: 
alpar@899:     ///Returns a const reference to the NodeMap \c potential (the dual solution).
alpar@899: 
alpar@899:     ///Returns a const reference to the NodeMap \c potential (the dual solution).
alpar@899:     /// \pre \ref run() must be called before using this function.
alpar@899:     const PotentialMap &getPotential() const { return potential;}
alpar@899: 
alpar@899:     /// Checking the complementary slackness optimality criteria
alpar@899: 
alpar@899:     ///This function checks, whether the given solution is optimal
alpar@899:     ///If executed after the call of \c run() then it should return with true.
alpar@899:     ///This function only checks optimality, doesn't bother with feasibility.
alpar@899:     ///It is meant for testing purposes.
alpar@899:     ///
alpar@899:     bool checkComplementarySlackness(){
alpar@899:       Length mod_pot;
alpar@899:       Length fl_e;
alpar@899:         for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) {
alpar@899: 	//C^{\Pi}_{i,j}
alpar@899: 	mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
alpar@899: 	fl_e = flow[e];
alpar@899: 	if (0<fl_e && fl_e<capacity[e]) {
alpar@899: 	  /// \todo better comparison is needed for real types, moreover, 
alpar@899: 	  /// this comparison here is superfluous.
alpar@899: 	  if (mod_pot != 0)
alpar@899: 	    return false;
alpar@899: 	} 
alpar@899: 	else {
alpar@899: 	  if (mod_pot > 0 && fl_e != 0)
alpar@899: 	    return false;
alpar@899: 	  if (mod_pot < 0 && fl_e != capacity[e])
alpar@899: 	    return false;
alpar@899: 	}
alpar@899:       }
alpar@899:       return true;
alpar@899:     }
alpar@899:     
alpar@899: 
alpar@899:   }; //class MinCostFlow
alpar@899: 
alpar@899:   ///@}
alpar@899: 
alpar@921: } //namespace lemon
alpar@899: 
alpar@921: #endif //LEMON_MIN_COST_FLOW_H