Graph partitioning using single commodity flows

We show that the sparsest cut in graphs with <i>n</i> vertices and <i>m</i> edges can be approximated within <i>O</i>(log<sup>2</sup> <i>n</i>) factor in Õ(<i>m</i> + n<sup>3/2</sup>) time using polylogarithmic single commodity max-flow computations. Previous algorithms are based on multicommodity flows that take time Õ(<i>m</i> + n<sup>2</sup>). Our algorithm iteratively employs max-flow computations to embed an expander flow, thus providing a certificate of expansion. Our technique can also be extended to yield an <i>O</i>(log<sup>2</sup> <i>n</i>)-(pseudo-) approximation algorithm for the edge-separator problem with a similar running time.

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