Quiet planting in the locked constraints satisfaction problems
Lenka Zdeborová, Florent Krząkała · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2009
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, thus providing hard satisfiable benchmarks. In a part of that hard region instances have with high probability a single satisfying assignment.