, Volume 19, Issue 4, pp 390–410

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

  • B. V. Cherkassky
  • A. V. Goldberg

DOI: 10.1007/PL00009180

Cite this article as:
Cherkassky, B. & Goldberg, A. Algorithmica (1997) 19: 390. doi:10.1007/PL00009180


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.

Copyright information

© 1997 Springer-Verlag New York Inc.

Authors and Affiliations

  • B. V. Cherkassky
    • 1
  • A. V. Goldberg
    • 2
  1. 1.Central Institute for Economics and Mathematics, Krasikova St. 32, 117418 Moscow, Russia.
  2. 2.Computer Science Department, Stanford University, Stanford, CA 94305, USA. Current address: NEC Research Institute Inc., 4 Independence Way, Princeton, NJ 08540, USA.