O(root log n) APPROXIMATION TO SPARSEST CUT IN (O)over-bar(n(2)) TIME

This paper shows how to compute O(root log n)-approximations to the SPARSEST CUT and BALANCED SEPARATOR problems in (O) over tilde (n(2)) time, thus improving upon the recent algorithm of Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231]. Their algorithm uses semidefinite programming and requires (O) over tilde (n(9.5)) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander flows was also established by Arora, Rao, and Vazirani [Proceedings of the 36th Annual ACM Symposium on Theory of Computing, 2004, pp. 222-231].