Improved approximation for directed cut problems

Authors:
Amit Agarwal;Noga Alon;Moses S. Charikar
Affiliations:
Princeton University, Princeton, NJ;Tel Aviv University, Tel Aviv, Israel;Princeton University, Princeton, NJ
Venue:
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Year:
2007

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Abstract

We present improved approximation algorithms for directed multicutand directed sparsest cut. The current best known approximationratio for these problems is O(n1/2). We obtain an Õ(n11/23)-approximation. Our algorithm works with thenatural LP relaxation used in prior work. We use a randomized roundingalgorithm with a more sophisticated charging scheme and analysis toobtain our improvement. This also implies a Õ(n11/23) upper bound on the ratio between the maximum multicommodity flowand minimum multicut in directed graphs.