, Volume 19, Issue 4, pp 390-410

First online:

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

  • B. V. CherkasskyAffiliated withCentral Institute for Economics and Mathematics, Krasikova St. 32, 117418 Moscow, Russia.
  • , A. V. GoldbergAffiliated withComputer Science Department, Stanford University, Stanford, CA 94305, USA. Current address: NEC Research Institute Inc., 4 Independence Way, Princeton, NJ 08540, USA.

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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.

Key words. Algorithms, Network optimization, Maximum flows, Experimental evaluation.