License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.49
URN: urn:nbn:de:0030-drops-101420
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10142/
Kothari, Pravesh K. ;
O'Donnell, Ryan ;
Schramm, Tselil
SOS Lower Bounds with Hard Constraints: Think Global, Act Local
Abstract
Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a "cardinality constraint", as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value beta, it did not necessarily actually "satisfy" the constraint "objective = beta". In this paper we show how to remedy both deficiencies in the case of random CSPs, by translating global constraints into local constraints. Using these ideas, we also show that degree-Omega(sqrt{n}) SOS does not provide a (4/3 - epsilon)-approximation for Min-Bisection, and degree-Omega(n) SOS does not provide a (11/12 + epsilon)-approximation for Max-Bisection or a (5/4 - epsilon)-approximation for Min-Bisection. No prior SOS lower bounds for these problems were known.
BibTeX - Entry
@InProceedings{kothari_et_al:LIPIcs:2018:10142,
author = {Pravesh K. Kothari and Ryan O'Donnell and Tselil Schramm},
title = {{SOS Lower Bounds with Hard Constraints: Think Global, Act Local}},
booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
pages = {49:1--49:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-095-8},
ISSN = {1868-8969},
year = {2018},
volume = {124},
editor = {Avrim Blum},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/10142},
URN = {urn:nbn:de:0030-drops-101420},
doi = {10.4230/LIPIcs.ITCS.2019.49},
annote = {Keywords: sum-of-squares hierarchy, random constraint satisfaction problems}
}
Keywords: |
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sum-of-squares hierarchy, random constraint satisfaction problems |
Collection: |
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10th Innovations in Theoretical Computer Science Conference (ITCS 2019) |
Issue Date: |
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2018 |
Date of publication: |
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08.01.2019 |