A fast cost scaling algorithm for submodular flow

Abstract This paper presents the current fastest known weakly polynomial algorithm for the submodular flow problem when the costs are not too big. It combines Rock's or Bland and Jensen's cost scaling algorithms, Cunningham and Frank's primal-dual algorithm for submodular flow, and Fujishige and Zhang's push/relabel algorithm for submodular maximum flow to get a running time of O (n 4 h log C) , where n is the number of nodes, C is the largest absolute value of arc costs and h is the time for computing an exchange capacity in an instance of this problem.

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