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

We give an O (root n)-approximation algorithm for the Sparsest Cut Problem on directed graphs. A naive reduction from Sparsest Cut to Minimum Multicut would only give an approximation ratio of O(root n log D), 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. (c) 2005 Elsevier B.V. All rights reserved.