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Locked constraint satisfaction problems (0803.2955v2)
Published 20 Mar 2008 in cond-mat.stat-mech, cond-mat.dis-nn, and cs.CC
Abstract: We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the phase diagram can be found easily, these problems, in their clustered phase, are extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions. We thus propose new benchmarks of really hard optimization problems and provide insight into the origin of their typical hardness.