An O(log k) approximate min-cut max-flow theorem and approximation algorithm

Yonatan Aumann*, Yuval Rabani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

201 Scopus citations

Abstract

It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for k-commodity flow instances with arbitrary capacities and demands. This improves upon the previously best-known bound of O(log2 k) and is existentially tight, up to a constant factor. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal min-cut ratio, is presented.

Original languageAmerican English
Pages (from-to)291-301
Number of pages11
JournalSIAM Journal on Computing
Volume27
Issue number1
DOIs
StatePublished - Feb 1998
Externally publishedYes

Keywords

  • Approximation algorithms
  • Cuts
  • Multicommodity flow
  • Network flow
  • Sparse cuts

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