diff -r ff46747676ed -r 1a8a66b6c6ce lemon/ssp_min_cost_flow.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/lemon/ssp_min_cost_flow.h	Mon Oct 30 17:22:14 2006 +0000
@@ -0,0 +1,260 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2006
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_MIN_COST_FLOW_H
+#define LEMON_MIN_COST_FLOW_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 <lemon/dijkstra.h>
+#include <lemon/graph_adaptor.h>
+#include <lemon/maps.h>
+#include <vector>
+
+namespace lemon {
+
+  /// \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 two nodes
+  /// 
+  ///
+  /// The \ref lemon::SspMinCostFlow "Successive Shortest Path Minimum
+  /// Cost Flow" 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 a directed graph with a cost function on
+  /// the edges. To this end, the edge-capacities and edge-costs have
+  /// to be nonnegative.  The edge-capacities should be integers, but
+  /// the edge-costs can be integers, reals or of other comparable
+  /// numeric type.  This algorithm is intended to be used 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 SspMinCostFlow {
+
+    typedef typename LengthMap::Value Length;
+
+    //Warning: this should be integer type
+    typedef typename CapacityMap::Value 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 ResGraphAdaptor<const Graph,int,CapacityMap,EdgeIntMap> ResGW;
+    typedef typename ResGW::Edge ResGraphEdge;
+
+  protected:
+
+    const Graph& g;
+    const LengthMap& length;
+    const CapacityMap& capacity;
+
+    EdgeIntMap flow; 
+    typedef typename Graph::template NodeMap<Length> PotentialMap;
+    PotentialMap potential;
+
+    Node s;
+    Node t;
+    
+    Length total_length;
+
+    class ModLengthMap {   
+      typedef typename Graph::template NodeMap<Length> NodeMap;
+      const ResGW& g;
+      const LengthMap &length;
+      const NodeMap &pot;
+    public :
+      typedef typename LengthMap::Key Key;
+      typedef typename LengthMap::Value Value;
+
+      ModLengthMap(const ResGW& _g, 
+		   const LengthMap &_length, const NodeMap &_pot) : 
+	g(_g), /*rev(_rev),*/ length(_length), pot(_pot) { }
+	
+      Value operator[](typename ResGW::Edge e) const {     
+	if (g.forward(e))
+	  return  length[e]-(pot[g.target(e)]-pot[g.source(e)]);   
+	else
+	  return -length[e]-(pot[g.target(e)]-pot[g.source(e)]);   
+      }     
+	
+    }; //ModLengthMap
+
+    ResGW res_graph;
+    ModLengthMap mod_length;
+    Dijkstra<ResGW, ModLengthMap> dijkstra;
+
+  public :
+
+    /// \brief The constructor of the class.
+    ///
+    /// \param _g The directed graph the algorithm runs on. 
+    /// \param _length The length (cost) of the edges. 
+    /// \param _cap The capacity of the edges. 
+    /// \param _s Source node.
+    /// \param _t Target node.
+    SspMinCostFlow(Graph& _g, LengthMap& _length, CapacityMap& _cap, 
+                   Node _s, Node _t) : 
+      g(_g), length(_length), capacity(_cap), flow(_g), potential(_g), 
+      s(_s), t(_t), 
+      res_graph(g, capacity, flow), 
+      mod_length(res_graph, length, potential),
+      dijkstra(res_graph, mod_length) { 
+      reset();
+    }
+    
+    /// \brief Tries to augment the flow between s and t by 1. The
+    /// return value shows if the augmentation is successful.
+    bool augment() {
+      dijkstra.run(s);
+      if (!dijkstra.reached(t)) {
+
+	//Unsuccessful augmentation.
+	return false;
+      } else {
+
+	//We have to change the potential
+	for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n)
+	  potential.set(n, potential[n]+dijkstra.distMap()[n]);
+	
+	//Augmenting on the shortest path
+	Node n=t;
+	ResGraphEdge e;
+	while (n!=s){
+	  e = dijkstra.predEdge(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 true;
+      }
+    }
+    
+    /// \brief Runs the algorithm.
+    ///
+    /// Runs the algorithm.
+    /// Returns k if there is a flow of value at least k from s to t.
+    /// Otherwise it returns the maximum value of a flow from s to t.
+    ///
+    /// \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.
+    ///
+    /// \todo If the actual flow value is bigger than k, then
+    /// everything is cleared and the algorithm starts from zero
+    /// flow. Is it a good approach?
+    int run(int k) {
+      if (flowValue()>k) reset();
+      while (flowValue()<k && augment()) { }
+      return flowValue();
+    }
+
+    /// \brief The class is reset to zero flow and potential. The
+    /// class is reset to zero flow and potential.
+    void reset() {
+      total_length=0;
+      for (typename Graph::EdgeIt e(g); e!=INVALID; ++e) flow.set(e, 0);
+      for (typename Graph::NodeIt n(g); n!=INVALID; ++n) potential.set(n, 0);  
+    }
+
+    /// \brief Returns the value of the actual flow. 
+    int flowValue() const {
+      int i=0;
+      for (typename Graph::OutEdgeIt e(g, s); e!=INVALID; ++e) i+=flow[e];
+      for (typename Graph::InEdgeIt e(g, s); e!=INVALID; ++e) i-=flow[e];
+      return i;
+    }
+
+    /// \brief Total cost of the found flow.
+    ///
+    /// This function gives back the total cost of the found flow.
+    Length totalLength(){
+      return total_length;
+    }
+
+    /// \brief Returns a const reference to the EdgeMap \c flow. 
+    ///
+    /// Returns a const reference to the EdgeMap \c flow. 
+    const EdgeIntMap &getFlow() const { return flow;}
+
+    /// \brief Returns a const reference to the NodeMap \c potential
+    /// (the dual solution).
+    ///
+    /// Returns a const reference to the NodeMap \c potential (the
+    /// dual solution).
+    const PotentialMap &getPotential() const { return potential;}
+
+    /// \brief Checking the complementary slackness optimality criteria.
+    ///
+    /// This function checks, whether the given flow and potential 
+    /// satisfy the complementary slackness conditions (i.e. these are optimal).
+    /// This function only checks optimality, doesn't bother with feasibility.
+    /// For testing purpose.
+    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.target(e)]+potential[g.source(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 SspMinCostFlow
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_MIN_COST_FLOW_H