Abstract
We show how to compute 0(\sqrt {\log n)}-approximations to SPARSEST CUT and BALANCED SEPARATOR problems in ?(n²) time, thus improving upon the recent algorithm of Arora, Rao and Vazirani (2004). Their algorithm uses semidefinite programming and required ?(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.