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.ICALP.2016.65
URN: urn:nbn:de:0030-drops-62197
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6219/
Hetterich, Samuel
Analysing Survey Propagation Guided Decimationon Random Formulas
Abstract
Let vec(theta) be a uniformly distributed random k-SAT formula with n variables and m clauses. For clauses/variables ratio m/n <= r_{k-SAT} ~ 2^k*ln(2) the formula vec(theta) is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond m/n ~ 2k*ln(k)/k with a non-vanishing probability. Non-rigorous statistical mechanics work on k-CNF led to the development of a new efficient "message passing algorithm" called Survey Propagation Guided Decimation [Mézard et al., Science 2002]. Experiments conducted for k=3,4,5 suggest that the algorithm finds satisfying assignments close to r_{k-SAT}. However, in the present paper we prove that the basic version of Survey Propagation Guided Decimation fails to solve random k-SAT formulas efficiently already for m/n = 2^{k}(1 + epsilon_k)*ln(k)/k with lim_{k -> infinity} epsilon_k = 0 almost a factor k below r_{k-SAT}.
BibTeX - Entry
@InProceedings{hetterich:LIPIcs:2016:6219,
author = {Samuel Hetterich},
title = {{Analysing Survey Propagation Guided Decimationon Random Formulas}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {65:1--65:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6219},
URN = {urn:nbn:de:0030-drops-62197},
doi = {10.4230/LIPIcs.ICALP.2016.65},
annote = {Keywords: Survey Propagation Guided Decimation, Message Passing Algorithm, Graph Theory, Random k-SAT}
}
Keywords: |
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Survey Propagation Guided Decimation, Message Passing Algorithm, Graph Theory, Random k-SAT |
Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
Issue Date: |
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2016 |
Date of publication: |
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23.08.2016 |