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29 March 2024
 
  » arxiv » 1304.3365

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Towards a better approximation for sparsest cut?
Sanjeev Arora ; Rong Ge ; Ali Kemal Sinop ;
Date 11 Apr 2013
AbstractWe give a new $(1+epsilon)$-approximation for sparsest cut problem on graphs where small sets expand significantly more than the sparsest cut (sets of size $n/r$ expand by a factor $sqrt{log nlog r}$ bigger, 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 {em Small Set Expander Flows} (inspired by the {em expander flows} of ARV) which we show exists in the input graph. Both algorithms run in time $2^{O(r)} mathrm{poly}(n)$. 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 $(1+epsilon)$-approximation on such general family of graphs.
Source arXiv, 1304.3365
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