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

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

2009-11-23

arxiv.org/abs/0911.4328v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 4 figures, final version as accepted by International Journal of Modern Physics B

Scientific paper

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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