Constraint satisfaction problems with isolated solutions are hard

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dc.creatorZdeborová, Lenka
dc.creatorMézard, Marc
dc.date2008-10-08
dc.date2008-12-04
dc.date.accessioned2026-07-07T12:09:57Z
dc.date.available2026-07-07T12:09:57Z
dc.descriptionWe study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The special property of the locked problems is that clusters of solutions are isolated points. This simplifies significantly the determination of the phase diagram, which makes the locked problems particularly appealing from the mathematical point of view. On the other hand we show empirically that the clustered phase of these problems is extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions. Our results suggest that the easy/hard transition (for currently known algorithms) in the locked problems coincides with the clustering transition. These should thus be regarded as new benchmarks of really hard constraint satisfaction problems.
dc.description19 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0810.1499
dc.identifierhttp://arxiv.org/abs/0810.1499
dc.identifierJ. Stat. Mech. (2008) P12004
dc.identifierdoi:10.1088/1742-5468/2008/12/P12004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209802
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subjectComputational Complexity
dc.subjectData Structures and Algorithms
dc.titleConstraint satisfaction problems with isolated solutions are hard
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