The complexity status of problems related to sparsest cuts
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Ranking with submodular valuations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of finding uniform sparsest cuts in various graph classes
Journal of Discrete Algorithms
d-dimensional arrangement revisited
Information Processing Letters
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This paper shows how to compute $O(\sqrt{\log n})$-approximations to the Sparsest Cut and Balanced Separator problems in $\tilde{O}(n^2)$ 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 $\tilde{O}(n^{9.5})$ 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].