Sanjeev Arora, Elad Hazan and Satyen Kale
In SIAM Journal on Computing (SICOMP), 2010. Also in proceedings of 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), 2004

We show how to compute $$O(\sqrt{\log n})$$-approximations to SPARSEST CUT and BALANCED SEPARATOR problems in $$\tilde{O}(n^2)$$ time, thus improving upon the recent algorithm of Arora, Rao and Vazirani (2004). Their algorithm uses semidefinite programming and required $$\tilde{O}(n^{4.5})$$ 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.