@MISC{Eppstein00clusteringfor, author = {David Eppstein}, title = {Clustering for Faster Network Simplex Pivots}, year = {2000} }

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Abstract

We show how to use a combination of tree-clustering techniques and computational geometry to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimum-cost flow and related problems and for pivot execution in the dual network simplex algorithm, from O(m) to O (√m) per pivot. Our techniques can also speed up network simplex algorithms for generalized flow, shortest paths with negative edges, maximum flow, the assignment problem, and the transshipment problem.