source: lemon-0.x/src/work/athos/mincostflow.h @ 657:531fc5f575ef

// -*- c++ -*-
#ifndef HUGO_MINCOSTFLOW_H
#define HUGO_MINCOSTFLOW_H

///\ingroup galgs
///\file
///\brief An algorithm for finding the minimum cost flow of given value in an uncapacitated network

#include <hugo/dijkstra.h>
#include <hugo/graph_wrapper.h>
#include <hugo/maps.h>
#include <vector>
#include <list>
#include <for_each_macros.h>
#include <hugo/union_find.h>

namespace hugo {

/// \addtogroup galgs
/// @{

  ///\brief Implementation of an algorithm for finding the minimum cost flow 
  /// of given value in an uncapacitated network
  /// 
  ///
  /// The class \ref hugo::MinCostFlow "MinCostFlow" implements
  /// an algorithm for solving the following general minimum cost flow problem>
  /// 
  ///
  ///
  /// \warning It is assumed here that the problem has a feasible solution
  ///
  /// The range of the length (weight) function is nonnegative reals but 
  /// the range of capacity function is the set of nonnegative integers. 
  /// It is not a polinomial time algorithm for counting the minimum cost
  /// maximal flow, since it counts the minimum cost flow for every value 0..M
  /// where \c M is the value of the maximal flow.
  ///
  ///\author Attila Bernath
  template <typename Graph, typename LengthMap, typename SupplyDemandMap>
  class MinCostFlow {

    typedef typename LengthMap::ValueType Length;


    typedef typename SupplyDemandMap::ValueType SupplyDemand;
    
    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 ConstMap<Edge,int> ConstMap;

    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;
    typedef typename ResGraphType::Edge ResGraphEdge;

    class ModLengthMap {   
      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;
      typedef typename Graph::template NodeMap<Length> NodeMap;
      const ResGraphType& G;
      //      const EdgeIntMap& rev;
      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 SupplyDemandMap& supply_demand;//supply or demand of nodes


    //auxiliary variables

    //To store the flow
    EdgeIntMap flow; 
    //To store the potentila (dual variables)
    typename Graph::template NodeMap<Length> potential;
    //To store excess-deficit values
    SupplyDemandMap excess_deficit;
    

    Length total_length;


  public :


    MinCostFlow(Graph& _G, LengthMap& _length, SupplyDemandMap& _supply_demand) : G(_G), 
      length(_length), supply_demand(_supply_demand), flow(_G), potential(_G){ }

    
    ///Runs the algorithm.

    ///Runs the algorithm.

    ///\todo May be it does make sense to be able to start with a nonzero 
    /// feasible primal-dual solution pair as well.
    int run() {

      //Resetting variables from previous runs
      //total_length = 0;

      typedef typename Graph::template NodeMap<int> HeapMap;
      typedef Heap< Node, SupplyDemand, typename Graph::template NodeMap<int>,
        std::greater<SupplyDemand> >    HeapType;

      //A heap for the excess nodes
      HeapMap excess_nodes_map(G,-1);
      HeapType excess_nodes(excess_nodes_map);

      //A heap for the deficit nodes
      HeapMap deficit_nodes_map(G,-1);
      HeapType deficit_nodes(deficit_nodes_map);

      //A container to store nonabundant arcs
      list<Edge> nonabundant_arcs;
      
      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
        flow.set(e,0);
        nonabundant_arcs.push_back(e);
      }

      //Initial value for delta
      SupplyDemand delta = 0;

      typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;

      //A union-find structure to store the abundant components
      UFE::MapType abund_comp_map(G);
      UFE abundant_components(abund_comp_map);



      FOR_EACH_LOC(typename Graph::NodeIt, n, G){
        excess_deficit.set(n,supply_demand[n]);
        //A supply node
        if (excess_deficit[n] > 0){
          excess_nodes.push(n,excess_deficit[n]);
        }
        //A demand node
        if (excess_deficit[n] < 0){
          deficit_nodes.push(n, - excess_deficit[n]);
        }
        //Finding out starting value of delta
        if (delta < abs(excess_deficit[n])){
          delta = abs(excess_deficit[n]);
        }
        //Initialize the copy of the Dijkstra potential to zero
        potential.set(n,0);
        //Every single point is an abundant component initially 
        abundant_components.insert(n);
      }

      //It'll be allright as an initial value, though this value 
      //can be the maximum deficit here
      SupplyDemand max_excess = delta;
      
      //We need a residual graph which is uncapacitated
      ResGraphType res_graph(G, flow);


      
      ModLengthMap mod_length(res_graph, length, potential);

      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);


      while (max_excess > 0){

        //Reset delta if still too big
        if (8*number_of_nodes*max_excess <= delta){
          delta = max_excess;
          
        }

        /*
         * Beginning of the delta scaling phase 
        */
        //Merge and stuff
        {
          SupplyDemand buf=8*number_of_nodes*delta;
          list<Edge>::iterator i = nonabundant_arcs.begin();
          while ( i != nonabundant_arcs.end() ){
            if (flow[i]>=buf){
              Node a = abundant_components.find(res_graph.head(i));
              Node b = abundant_components.find(res_graph.tail(i));
              //Merge
              if (a != b){
                //Find path and augment
                //!!!
                //Find path and augment
                abundant_components.join(a,b);
              }
              //What happens to i?
              nonabundant_arcs.erase(i);
            }
            else
              ++i;
          }
        }


        Node s = excess_nodes.top(); 
        SupplyDemand max_excess = excess_nodes[s];
        Node t = deficit_nodes.top(); 
        if (max_excess < dificit_nodes[t]){
          max_excess = dificit_nodes[t];
        }


        while(max_excess > 0){

          
          //s es t valasztasa

          //Dijkstra part       
          dijkstra.run(s);

          /*We know from theory that t can be reached
          if (!dijkstra.reached(t)){
            //There are no k paths from s to t
            break;
          };
          */
          
          //We have to change the potential
          FOR_EACH_LOC(typename ResGraphType::NodeIt, n, res_graph){
            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,delta);
            /*
            //Let's update the total length
            if (res_graph.forward(e))
              total_length += length[e];
            else 
              total_length -= length[e];            
            */
          }

          //Update the excess_nodes heap
          if (delta >= excess_nodes[s]){
            if (delta > excess_nodes[s])
              deficit_nodes.push(s,delta - excess_nodes[s]);
            excess_nodes.pop();
            
          } 
          else{
            excess_nodes[s] -= delta;
          }
          //Update the deficit_nodes heap
          if (delta >= deficit_nodes[t]){
            if (delta > deficit_nodes[t])
              excess_nodes.push(t,delta - deficit_nodes[t]);
            deficit_nodes.pop();
            
          } 
          else{
            deficit_nodes[t] -= delta;
          }
          //Dijkstra part ends here
        }

        /*
         * End of the delta scaling phase 
        */

        //Whatever this means
        delta = delta / 2;

        /*This is not necessary here
        //Update the max_excess
        max_excess = 0;
        FOR_EACH_LOC(typename Graph::NodeIt, n, G){
          if (max_excess < excess_deficit[n]){
            max_excess = excess_deficit[n];
          }
        }
        */

          
      }//while(max_excess > 0)
      

      return i;
    }




    ///This function gives back the total length of the found paths.
    ///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. \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).
    /// \pre \ref run() must be called before using this function.
    const EdgeIntMap &getPotential() const { return potential;}

    ///This function checks, whether the given solution is optimal
    ///Running after a \c run() should return with true
    ///In this "state of the art" this only check optimality, doesn't bother with feasibility
    ///
    ///\todo Is this OK here?
    bool checkComplementarySlackness(){
      Length mod_pot;
      Length fl_e;
      FOR_EACH_LOC(typename Graph::EdgeIt, e, G){
        //C^{\Pi}_{i,j}
        mod_pot = length[e]-potential[G.head(e)]+potential[G.tail(e)];
        fl_e = flow[e];
        //      std::cout << fl_e << std::endl;
        if (0<fl_e && fl_e<capacity[e]){
          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_MINCOSTFLOW_H