Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.105
URN: urn:nbn:de:0030-drops-46911
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4691/
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: | 04.09.2014 |
