Balanced Random Constraint Satisfaction: Phase Transition and Hardness

Two models of nearly balanced random constraint satisfaction problems, called Model NB and UB respectively, are defined in this paper. By nearly balanced it means that most variables appear in the same number of constraints. Exact satisfiability thresholds for these models are proven, which are of the same values as that for Model RB. Experiments on random instances around the thresholds for these three models are conducted. The results show that these balanced models are much harder to solve than their unbalanced counterpart.

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