Performances of pure random walk algorithms on constraint satisfaction problems with growing domains

The performances of two types of pure random walk (PRW) algorithms for a model of constraint satisfaction problem with growing domains (called Model RB) are investigated. Threshold phenomenons appear for both algorithms. In particular, when the constraint density $$r$$r is smaller than a threshold value $$r_d$$rd, PRW algorithms can solve instances of Model RB efficiently, but when $$r$$r is bigger than the $$r_d$$rd, they fail. Using a physical method, we find out the threshold values for both algorithms. When the number of variables $$N$$N is large, the threshold values tend to zero, so generally speaking PRW does not work on Model RB. By performing experiments, we show that PRW strategy cannot do better than other fundamental strategies.

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