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kpeter (Peter Kovacs)
kpeter@inf.elte.hu
Add citations to the scaling MCF algorithms (#180, #184) and improve the doc of their group.
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doc/groups.dox
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lemon/capacity_scaling.h
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lemon/cost_scaling.h
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doc/groups.dox
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problem and its dual solution, see \ref min_cost_flow
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"Minimum Cost Flow Problem".
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LEMON contains several algorithms for this problem.


			




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 - \ref NetworkSimplex Primal Network Simplex algorithm with various


			




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   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.


			




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 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on


			




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   cost scaling \ref goldberg90approximation, \ref goldberg97efficient,


			




	
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 - \ref CostScaling Cost Scaling algorithm based on push/augment and


			




	
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   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,


			




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   \ref bunnagel98efficient.


			




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 - \ref CapacityScaling Successive Shortest %Path algorithm with optional


			




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   capacity scaling \ref edmondskarp72theoretical.


			




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 - \ref CancelAndTighten The Cancel and Tighten algorithm


			




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   \ref goldberg89cyclecanceling.


			




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 - \ref CycleCanceling Cycle-Canceling algorithms


			




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   \ref klein67primal, \ref goldberg89cyclecanceling.


			




	
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 - \ref CapacityScaling Capacity Scaling algorithm based on the successive


			




	
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   shortest path method \ref edmondskarp72theoretical.


			




	
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 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are


			




	
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   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.


			




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In general NetworkSimplex is the most efficient implementation,


			




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but in special cases other algorithms could be faster.


			




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For example, if the total supply and/or capacities are rather small,


			




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CapacityScaling is usually the fastest algorithm (without effective scaling).


			




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*/

			




        

    

    

    

        

            

                

                    lemon/capacity_scaling.h
                

                

                  
                  
                  
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  /// \brief Implementation of the Capacity Scaling algorithm for


			




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  /// finding a \ref min_cost_flow "minimum cost flow".


			




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  ///


			




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  /// \ref CapacityScaling implements the capacity scaling version


			




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  /// of the successive shortest path algorithm for finding a


			




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  /// \ref min_cost_flow "minimum cost flow". It is an efficient dual


			




	
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  /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,


			




	
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  /// \ref edmondskarp72theoretical. It is an efficient dual


			




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  /// solution method.


			




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  ///


			




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  /// Most of the parameters of the problem (except for the digraph)


			




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  /// can be given using separate functions, and the algorithm can be


			




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  /// executed using the \ref run() function. If some parameters are not


			




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  /// specified, then default values will be used.

			




        

    

    

    

        

            

                

                    lemon/cost_scaling.h
                

                

                  
                  
                  
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  /// @{


			




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  /// \brief Implementation of the Cost Scaling algorithm for


			




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  /// finding a \ref min_cost_flow "minimum cost flow".


			




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  ///


			




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  /// \ref CostScaling implements a cost scaling algorithm that performs


			




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  /// push/augment and relabel operations for finding a minimum cost


			




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  /// flow. It is an efficient primal-dual solution method, which


			




	
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  /// push/augment and relabel operations for finding a \ref min_cost_flow


			




	
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  /// "minimum cost flow" \ref amo93networkflows, \ref goldberg90approximation,


			




	
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  /// \ref goldberg97efficient, \ref bunnagel98efficient. 


			




	
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  /// It is a highly efficient primal-dual solution method, which


			




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  /// can be viewed as the generalization of the \ref Preflow


			




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  /// "preflow push-relabel" algorithm for the maximum flow problem.


			




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  ///


			




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  /// Most of the parameters of the problem (except for the digraph)


			




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  /// can be given using separate functions, and the algorithm can be


			




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  /// executed using the \ref run() function. If some parameters are not


			




        

    






    
    



    


    

     
    
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