We give an O(\sqrt{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(\sqrt{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.
Keywords: approximation algorithms, directed graphs, sparsest cut, multicommodity flow.