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 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.

SIAM Journal on Discrete Mathematics