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Maximum flow is one of the important and classical combinatorial optimization problems. However, the time complexity of sequential maximum flow algorithms remains high. In this paper, we present a two-stage distributed parallel algorithm (TSDPA) with message passing interface to improve the computational performance. The strategy of TSDPA has two stages, which push excess flows separately along cheap and expensive paths identified by a new distance estimate function. In TSDPA, stage 1 enhances the parallel efficiency by omitting high-cost paths and decentralizing calculations, and stage 2 guarantees the achievement of an optimal solution through divide-and-conquer method. The experimental test demonstrates that TSDPA runs 1.2---15.5 times faster than sequential algorithms and is faster than or almost as fast as the H_PRF and Q_PRF codes.

Two-stage distributed parallel algorithm with message passing interface for maximum flow problem