diff -r c46cfb2651ec -r f485b3008cf5 src/hugo/min_cost_flow.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/hugo/min_cost_flow.h	Wed Sep 22 09:55:41 2004 +0000
@@ -0,0 +1,241 @@
+// -*- c++ -*-
+#ifndef HUGO_MINCOSTFLOWS_H
+#define HUGO_MINCOSTFLOWS_H
+
+///\ingroup flowalgs
+///\file
+///\brief An algorithm for finding a flow of value \c k (for small values of \c k) having minimal total cost 
+
+
+#include <hugo/dijkstra.h>
+#include <hugo/graph_wrapper.h>
+#include <hugo/maps.h>
+#include <vector>
+
+namespace hugo {
+
+/// \addtogroup flowalgs
+/// @{
+
+  ///\brief Implementation of an algorithm for finding a flow of value \c k 
+  ///(for small values of \c k) having minimal total cost between 2 nodes 
+  /// 
+  ///
+  /// The class \ref hugo::MinCostFlow "MinCostFlow" implements
+  /// an algorithm for finding a flow of value \c k 
+  /// having minimal total cost 
+  /// from a given source node to a given target node in an
+  /// edge-weighted directed graph. To this end, 
+  /// the edge-capacities and edge-weitghs have to be nonnegative. 
+  /// The edge-capacities should be integers, but the edge-weights can be 
+  /// integers, reals or of other comparable numeric type.
+  /// This algorithm is intended to use only for small values of \c k, 
+  /// since it is only polynomial in k, 
+  /// not in the length of k (which is log k). 
+  /// In order to find the minimum cost flow of value \c k it 
+  /// finds the minimum cost flow of value \c i for every 
+  /// \c i between 0 and \c k. 
+  ///
+  ///\param Graph The directed graph type the algorithm runs on.
+  ///\param LengthMap The type of the length map.
+  ///\param CapacityMap The capacity map type.
+  ///
+  ///\author Attila Bernath
+  template <typename Graph, typename LengthMap, typename CapacityMap>
+  class MinCostFlow {
+
+    typedef typename LengthMap::ValueType Length;
+
+    //Warning: this should be integer type
+    typedef typename CapacityMap::ValueType Capacity;
+    
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+    typedef typename Graph::Edge Edge;
+    typedef typename Graph::OutEdgeIt OutEdgeIt;
+    typedef typename Graph::template EdgeMap<int> EdgeIntMap;
+
+
+    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
+    typedef typename ResGraphType::Edge ResGraphEdge;
+
+    class ModLengthMap {   
+      typedef typename Graph::template NodeMap<Length> NodeMap;
+      const ResGraphType& G;
+      const LengthMap &ol;
+      const NodeMap &pot;
+    public :
+      typedef typename LengthMap::KeyType KeyType;
+      typedef typename LengthMap::ValueType ValueType;
+	
+      ValueType operator[](typename ResGraphType::Edge e) const {     
+	if (G.forward(e))
+	  return  ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
+	else
+	  return -ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   
+      }     
+	
+      ModLengthMap(const ResGraphType& _G,
+		   const LengthMap &o,  const NodeMap &p) : 
+	G(_G), /*rev(_rev),*/ ol(o), pot(p){}; 
+    };//ModLengthMap
+
+
+  protected:
+    
+    //Input
+    const Graph& G;
+    const LengthMap& length;
+    const CapacityMap& capacity;
+
+
+    //auxiliary variables
+
+    //To store the flow
+    EdgeIntMap flow; 
+    //To store the potential (dual variables)
+    typedef typename Graph::template NodeMap<Length> PotentialMap;
+    PotentialMap potential;
+    
+
+    Length total_length;
+
+
+  public :
+
+    /// The constructor of the class.
+    
+    ///\param _G The directed graph the algorithm runs on. 
+    ///\param _length The length (weight or cost) of the edges. 
+    ///\param _cap The capacity of the edges. 
+    MinCostFlow(Graph& _G, LengthMap& _length, CapacityMap& _cap) : G(_G), 
+      length(_length), capacity(_cap), flow(_G), potential(_G){ }
+
+    
+    ///Runs the algorithm.
+    
+    ///Runs the algorithm.
+    ///Returns k if there is a flow of value at least k edge-disjoint 
+    ///from s to t.
+    ///Otherwise it returns the maximum value of a flow from s to t.
+    ///
+    ///\param s The source node.
+    ///\param t The target node.
+    ///\param k The value of the flow we are looking for.
+    ///
+    ///\todo May be it does make sense to be able to start with a nonzero 
+    /// feasible primal-dual solution pair as well.
+    int run(Node s, Node t, int k) {
+
+      //Resetting variables from previous runs
+      total_length = 0;
+      
+      for (typename Graph::EdgeIt e(G); e!=INVALID; ++e) flow.set(e, 0);
+
+      //Initialize the potential to zero
+      for (typename Graph::NodeIt n(G); n!=INVALID; ++n) potential.set(n, 0);
+      
+      
+      //We need a residual graph
+      ResGraphType res_graph(G, capacity, flow);
+
+
+      ModLengthMap mod_length(res_graph, length, potential);
+
+      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);
+
+      int i;
+      for (i=0; i<k; ++i){
+	dijkstra.run(s);
+	if (!dijkstra.reached(t)){
+	  //There are no flow of value k from s to t
+	  break;
+	};
+	
+	//We have to change the potential
+        for(typename ResGraphType::NodeIt n(res_graph); n!=INVALID; ++n)
+	  potential[n] += dijkstra.distMap()[n];
+
+
+	//Augmenting on the sortest path
+	Node n=t;
+	ResGraphEdge e;
+	while (n!=s){
+	  e = dijkstra.pred(n);
+	  n = dijkstra.predNode(n);
+	  res_graph.augment(e,1);
+	  //Let's update the total length
+	  if (res_graph.forward(e))
+	    total_length += length[e];
+	  else 
+	    total_length -= length[e];	    
+	}
+
+	  
+      }
+      
+
+      return i;
+    }
+
+
+
+    /// Gives back the total weight of the found flow.
+
+    ///This function gives back the total weight of the found flow.
+    ///Assumes that \c run() has been run and nothing changed since then.
+    Length totalLength(){
+      return total_length;
+    }
+
+    ///Returns a const reference to the EdgeMap \c flow. 
+
+    ///Returns a const reference to the EdgeMap \c flow. 
+    ///\pre \ref run() must
+    ///be called before using this function.
+    const EdgeIntMap &getFlow() const { return flow;}
+
+    ///Returns a const reference to the NodeMap \c potential (the dual solution).
+
+    ///Returns a const reference to the NodeMap \c potential (the dual solution).
+    /// \pre \ref run() must be called before using this function.
+    const PotentialMap &getPotential() const { return potential;}
+
+    /// Checking the complementary slackness optimality criteria
+
+    ///This function checks, whether the given solution is optimal
+    ///If executed after the call of \c run() then it should return with true.
+    ///This function only checks optimality, doesn't bother with feasibility.
+    ///It is meant for testing purposes.
+    ///
+    bool checkComplementarySlackness(){
+      Length mod_pot;
+      Length fl_e;
+        for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) {
+	//C^{\Pi}_{i,j}
+	mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
+	fl_e = flow[e];
+	if (0<fl_e && fl_e<capacity[e]) {
+	  /// \todo better comparison is needed for real types, moreover, 
+	  /// this comparison here is superfluous.
+	  if (mod_pot != 0)
+	    return false;
+	} 
+	else {
+	  if (mod_pot > 0 && fl_e != 0)
+	    return false;
+	  if (mod_pot < 0 && fl_e != capacity[e])
+	    return false;
+	}
+      }
+      return true;
+    }
+    
+
+  }; //class MinCostFlow
+
+  ///@}
+
+} //namespace hugo
+
+#endif //HUGO_MINCOSTFLOWS_H