, Volume 19, Issue 4, pp 390-410

On Implementing the Push—Relabel Method for the Maximum Flow Problem

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Abstract.

We study efficient implementations of the push—relabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementations: we show that the highest-level selection strategy gives better results when combined with both global and gap relabeling heuristics. We also exhibit a family of problems for which the running time of all implementations we consider is quadratic.

Received October 24, 1994; revised April 25, 1995.