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arXiv · 0911.4328

Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction Problems

Haijun Zhou
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Abstract

Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this paper we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value alpha_cm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At alpha_cm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.

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Haijun Zhou. 2010-07-02. Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction Problems. https://doi.org/10.1142/s0217979210056013

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