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Feige, Uriel; Mossel, Elchanan; Vilenchik, Dan

doi:10.4086/toc.2013.v009a019

Cited by 3 publications

(1 citation statement)

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“…Phase transition phenomena in other types of CSPs are also investigated in [8,49,9] In planted random CSPs, a "planted assignment" is first drawn, and the constraints are then drawn at random so as to keep that planted assignment a satisfying one. Planted ensembles were investigated in [12,37,7,6,38,5], and at high density in [10,20,28]. In the planted setting, the probability of being satisfiable is always equal to one by construction, and a more relevant question is to determine the actual number of satisfying assignments.…”

Section: Introductionmentioning

confidence: 99%

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Abbé¹,

Montanari²

2015

Theory of Comput.

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This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSPs), as well as other structures motivated by coding theory and community detection problems. It is shown that under mild assumptions on the kernel and for sparse random graphs, the conditional entropy of the node variables given the edge variables concentrates. This implies in particular concentration results for the number of solutions in a broad class of planted CSPs, the existence of a threshold function for the disassortative stochastic block model, and the proof of a conjecture on parity check codes. It also establishes new connections among coding, clustering and satisfiability.

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Section: Introductionmentioning

confidence: 99%

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Abbé¹,

Montanari²

2015

Theory of Comput.

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Solving Non-uniform Planted and Filtered Random SAT Formulas Greedily

Friedrich

Neumann

Rothenberger

et al. 2021

Theory and Applications of Satisfiability Testing – SAT 2021

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Belief Propagation Guided Decimation Fails on Random Formulas

Coja-Oghlan

2017

J. ACM

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Let be a uniformly distributed random k-SAT formula with n variables and m clauses. Nonconstructive arguments show that is satisfiable for clause/variable ratios m/n ≤ r k−SAT ∼ 2 k ln 2 with high probability. Yet no efficient algorithm is known to find a satisfying assignment beyond m/n ∼ 2 k ln(k)/k with a nonvanishing probability. On the basis of deep but nonrigorous statistical mechanics ideas, a message passing algorithm called Belief Propagation Guided Decimation has been put forward (Mézard, Parisi, Zecchina: Science 2002; Braunstein, Mézard, Zecchina: Random Struc. Algorithm 2005). Experiments suggested that the algorithm might succeed for densities very close to r k−SAT for k = 3, 4, 5 (Kroc, Sabharwal, Selman: SAC 2009). Furnishing the first rigorous analysis of this algorithm on a nontrivial input distribution, in the present article we show that Belief Propagation Guided Decimation fails to solve random k-SAT formulas already for m/n = O(2 k /k), almost a factor of k below the satisfiability threshold r k−SAT. Indeed, the proof refutes a key hypothesis on which Belief Propagation Guided Decimation hinges for such m/n.

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Cited by 3 publications

References 20 publications

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Solving Non-uniform Planted and Filtered Random SAT Formulas Greedily

Belief Propagation Guided Decimation Fails on Random Formulas

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