An O(√n-approximation algorithm for directed sparsest cut

Mohammad Taghi Hajiaghayi, Harald Räcke

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We give an O(n)-approximation algorithm for the Sparsest Cut Problem on directed graphs. A naïve reduction from Sparsest Cut to Minimum Multicut would only give an approximation ratio of O(nlogD), where D is the sum of the demands. We obtain the improvement using a novel LP-rounding method for fractional Sparsest Cut, the dual of Maximum Concurrent Flow.

Original languageEnglish
Pages (from-to)156-160
Number of pages5
JournalInformation Processing Letters
Issue number4
StatePublished - 28 Feb 2006
Externally publishedYes


  • Approximation algorithms
  • Directed graphs
  • Multicommodity flow
  • Sparsest cut


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