An efficient implementation of the network simplex method

This paper describes an efficient implementation of the network simplex method for solving large sparse minimum-cost network flow problems. This is a single-phase implementation which employs an initial spanning tree of all artificial edges, a gradual penalty method for reducing infeasibilities and a sample pricing strategy which does not require adjacency-ordered edge lists. Data structures, algorithmic details and computational experience with a set of generated problems are presented. For the problems tested, the present implementation is found to be more efficient than other available implementations of the network simplex and primal-dual methods.

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