Date of Original Version



Conference Proceeding

Rights Management

© ACM, YYYY. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published at

Abstract or Description

We give a 2-approximation algorithm for the non-uniform Sparsest Cut problem that runs in time nO(k), where k is the treewidth of the graph. This improves on the previous 22k-approximation in time poly(n) 2O(k) due to Chlamtac et al. [18].

To complement this algorithm, we show the following hardness results: If the non-uniform Sparsest Cut has a ρ-approximation for series-parallel graphs (where ρ ≥ 1), then the MaxCut problem has an algorithm with approximation factor arbitrarily close to 1/ρ. Hence, even for such restricted graphs (which have treewidth 2), the Sparsest Cut problem is NP-hard to approximate better than 17/16 - ε for ε > 0; assuming the Unique Games Conjecture the hardness becomes 1/αGW - ε. For graphs with large (but constant) treewidth, we show a hardness result of 2 - ε assuming the Unique Games Conjecture.

Our algorithm rounds a linear program based on (a subset of) the Sherali-Adams lift of the standard Sparsest Cut LP. We show that even for treewidth-2 graphs, the LP has an integrality gap close to 2 even after polynomially many rounds of Sherali-Adams. Hence our approach cannot be improved even on such restricted graphs without using a stronger relaxation.





Published In

Proceedings of the ACM Symposium on Theory of Computing (STOC), 2013, 281-290.