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On the complexity of preflow-push algorithms for maximum-flow problems

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Abstract

We study the maximum-flow algorithm of Goldberg and Tarjan and show that the largest-label implementation runs inO(n 2 √m) time. We give a new proof of this fact. We compare our proof with the earlier work by Cheriyan and Maheswari who showed that the largest-label implementation of the preflow-push algorithm of Goldberg and Tarjan runs inO(n 2 √m) time when implemented with current edges. Our proof that the number of nonsaturating pushes isO(n 2 √m), does not rely on implementing pushes with current edges, therefore it is true for a much larger family of largest-label implementation of the preflow-push algorithms.

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References

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Levent Tunçel

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  1. Levent Tunçel
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Additional information

Communicated by Harold N. Gabow.

Research performed while the author was a Ph.D. student at Cornell University and was partially supported by the Ministry of Education of the Republic of Turkey through the scholarship program 1416.

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Tunçel, L. On the complexity of preflow-push algorithms for maximum-flow problems. Algorithmica 11, 353–359 (1994). https://doi.org/10.1007/BF01187018

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  • DOI: https://doi.org/10.1007/BF01187018

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