Quiet Planting in the Locked Constraint Satisfaction Problems

Details Quiet Planting in the Locked Constraint Satisfaction Problems Quiet Planting in the Locked Constraint Satisfaction Problems

2009-02-24

arxiv.org/abs/0902.4185v3

SIAM J. Discrete Math. 25, 750-770 (2011)

Physics

Condensed Matter

Statistical Mechanics

21 pages, revised version

Scientific paper

10.1137/090750755

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 first and second moment considerations; in particular the connection with the reconstruction on trees appears to be crucial. 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.

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