src/lemon/min_cost_flow.h
changeset 1270 806451fd084b
parent 1164 80bb73097736
child 1359 1581f961cfaa
     1.1 --- a/src/lemon/min_cost_flow.h	Mon Mar 28 23:34:26 2005 +0000
     1.2 +++ b/src/lemon/min_cost_flow.h	Tue Mar 29 07:35:09 2005 +0000
     1.3 @@ -36,20 +36,18 @@
     1.4    ///(for small values of \c k) having minimal total cost between 2 nodes 
     1.5    /// 
     1.6    ///
     1.7 -  /// The class \ref lemon::MinCostFlow "MinCostFlow" implements
     1.8 -  /// an algorithm for finding a flow of value \c k 
     1.9 -  /// having minimal total cost 
    1.10 -  /// from a given source node to a given target node in an
    1.11 -  /// edge-weighted directed graph. To this end, 
    1.12 -  /// the edge-capacities and edge-weitghs have to be nonnegative. 
    1.13 -  /// The edge-capacities should be integers, but the edge-weights can be 
    1.14 -  /// integers, reals or of other comparable numeric type.
    1.15 -  /// This algorithm is intended to use only for small values of \c k, 
    1.16 -  /// since it is only polynomial in k, 
    1.17 -  /// not in the length of k (which is log k). 
    1.18 -  /// In order to find the minimum cost flow of value \c k it 
    1.19 -  /// finds the minimum cost flow of value \c i for every 
    1.20 -  /// \c i between 0 and \c k. 
    1.21 +  /// The class \ref lemon::MinCostFlow "MinCostFlow" implements an
    1.22 +  /// algorithm for finding a flow of value \c k having minimal total
    1.23 +  /// cost from a given source node to a given target node in an
    1.24 +  /// edge-weighted directed graph. To this end, the edge-capacities
    1.25 +  /// and edge-weights have to be nonnegative.  The edge-capacities
    1.26 +  /// should be integers, but the edge-weights can be integers, reals
    1.27 +  /// or of other comparable numeric type.  This algorithm is intended
    1.28 +  /// to be used only for small values of \c k, since it is only
    1.29 +  /// polynomial in k, not in the length of k (which is log k):  in
    1.30 +  /// order to find the minimum cost flow of value \c k it finds the
    1.31 +  /// minimum cost flow of value \c i for every \c i between 0 and \c
    1.32 +  /// k.
    1.33    ///
    1.34    ///\param Graph The directed graph type the algorithm runs on.
    1.35    ///\param LengthMap The type of the length map.
    1.36 @@ -149,7 +147,7 @@
    1.37  	for(typename ResGW::NodeIt n(res_graph); n!=INVALID; ++n)
    1.38  	  potential.set(n, potential[n]+dijkstra.distMap()[n]);
    1.39  	
    1.40 -	//Augmenting on the sortest path
    1.41 +	//Augmenting on the shortest path
    1.42  	Node n=t;
    1.43  	ResGraphEdge e;
    1.44  	while (n!=s){
    1.45 @@ -226,7 +224,7 @@
    1.46      /*! \brief Checking the complementary slackness optimality criteria.
    1.47  
    1.48      This function checks, whether the given flow and potential 
    1.49 -    satisfiy the complementary slackness cnditions (i.e. these are optimal).
    1.50 +    satisfy the complementary slackness conditions (i.e. these are optimal).
    1.51      This function only checks optimality, doesn't bother with feasibility.
    1.52      For testing purpose.
    1.53      */