Towards a better approximation for SPARSEST CUT?

Journal Article

We give a new (1 + ε)-approximation for SPARSEST CUT problem on graphs where small sets expand significantly more than the sparsest cut (expansion of sets of size n/r exceeds that of the sparsest cut by a factor √ log n log r, for some small r; this condition holds for many natural graph families). We give two different algorithms. One involves Guruswami-Sinop rounding on the level-r Lasserre relaxation. The other is combinatorial and involves a new notion called Small Set Expander Flows (inspired by the expander flows of [1]) which we show exists in the input graph. Both algorithms run in time 2O(r)poly(n). We also show similar approximation algorithms in graphs with genus g with an analogous local expansion condition. This is the first algorithm we know of that achieves (1 + ε)-approximation on such general family of graphs. Copyright © 2013 by The Institute of Electrical and Electronics Engineers, Inc.

Full Text

Duke Authors

Cited Authors

  • Arora, S; Ge, R; Sinop, AK

Published Date

  • December 1, 2013

Published In

Start / End Page

  • 270 - 279

International Standard Serial Number (ISSN)

  • 0272-5428

Digital Object Identifier (DOI)

  • 10.1109/FOCS.2013.37

Citation Source

  • Scopus