Quiet Planting in the Locked Constraint Satisfaction Problems

We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and the first and second moment considerations. Our main result is the l...

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Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 25; no. 2; pp. 750 - 770
Main Authors Zdeborová, Lenka, Krzakala, Florent
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects
Algebra
Applied mathematics
Combinatorics
Combinatorics. Ordered structures
Computer science
Exact sciences and technology
Graph theory
Heuristic
Laboratories
Mathematics
Sciences and techniques of general use
Statistical physics
Variables
Reconstruction
68Q25
belief propagation
Propagation
Probability
Probability distribution
05C80
90C27
Assignment
constraint satisfaction problems
instances with a unique satisfying assignment
planted random ensemble
Ensemble
Discrete mathematics
Tree
reconstruction on trees
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ISSN0895-4801
1095-7146
DOI10.1137/090750755

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Summary:We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and the first and second moment considerations. Our main result is the location of the hard region in the planted ensemble. In a part of that hard region, instances have with high probability a single satisfying assignment. [PUBLICATION ABSTRACT]
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ISSN:0895-4801
1095-7146
DOI:10.1137/090750755