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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.105
URN: urn:nbn:de:0030-drops-46911
URL: http://drops.dagstuhl.de/opus/volltexte/2014/4691/
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Deshpande, Amit ; Venkat, Rakesh

Guruswami-Sinop Rounding without Higher Level Lasserre

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Abstract

Guruswami and Sinop give a O(1/delta) approximation guarantee for the non-uniform Sparsest Cut problem by solving O(r)-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and demand graphs satisfy a certain spectral condition, namely, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta). Their key idea is a rounding technique that first maps a vector-valued solution to [0,1] using appropriately scaled projections onto Lasserre vectors. In this paper, we show that similar projections and analysis can be obtained using only l_2^2 triangle inequality constraints. This results in a O(r/delta^2) approximation guarantee for the non-uniform Sparsest Cut problem by adding only l_2^2 triangle inequality constraints to the usual semidefinite program, provided that the same spectral condition, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta), holds.

BibTeX - Entry

@InProceedings{deshpande_et_al:LIPIcs:2014:4691,
  author =	{Amit Deshpande and Rakesh Venkat},
  title =	{{Guruswami-Sinop Rounding without Higher Level Lasserre}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{105--114},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4691},
  URN =		{urn:nbn:de:0030-drops-46911},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.105},
  annote =	{Keywords: Sparsest Cut, Lasserre Hierarchy, Metric embeddings}
}

Keywords: Sparsest Cut, Lasserre Hierarchy, Metric embeddings
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Issue Date: 2014
Date of publication: 02.09.2014


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