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# Analysing Survey Propagation Guided Decimationon Random Formulas

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LIPIcs.ICALP.2016.65.pdf
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## Cite As

Samuel Hetterich. Analysing Survey Propagation Guided Decimationon Random Formulas. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 65:1-65:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ICALP.2016.65

## 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}.
##### Keywords
• Survey Propagation Guided Decimation
• Message Passing Algorithm
• Graph Theory
• Random k-SAT

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