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|Abstract:||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 ) 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.|
|Citation:||Arora, S, Ge, R, Sinop, AK. (2013). Towards a better approximation for SPARSEST CUT?. 270 - 279. doi:10.1109/FOCS.2013.37|
|Pages:||270 - 279|
|Type of Material:||Conference Article|
|Journal/Proceeding Title:||Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS|
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