Graph partitioning using single commodity flows

Authors:
Rohit Khandekar;Satish Rao;Umesh Vazirani
Affiliations:
University of Waterloo, Canada;University of California, Berkeley;University of California, Berkeley
Venue:
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Year:
2006

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Abstract

We show that the sparsest cut in graphs can be approximated within O(log2 n) factor in Õ(n3/2) time using polylogarithmic single commodity max-flow computations. Previous algorithms are based on multicommodity flows which take time Õ(n2). 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 O(log2 n) (pseudo) approximation algorithm for the edge-separator problem with a similar running time.