Sparsest cut on bounded treewidth graphs: algorithms and hardness results

@inproceedings{Gupta2013SparsestCO,
  title={Sparsest cut on bounded treewidth graphs: algorithms and hardness results},
  author={Anupam Gupta and Kunal Talwar and David Witmer},
  booktitle={STOC},
  year={2013}
}
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… CONTINUE READING
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