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

Authors:
Mohammad Taghi Hajiaghayi;Harald Räcke
Affiliations:
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA;School of Computer Science, Carnegie Mellon University, Pittsburgh, PA
Venue:
Information Processing Letters
Year:
2006

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Abstract

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.