A Study 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 problems with growing domains (called Model RB) are investigated. Threshold phenomenons appear for both algorithms. In particular, when the constraint density r is smaller than a threshold value r(d), PRW algorithms can solve instances of Model RB efficiently, but when r is bigger than the rd, they fail. Using a physical method, we find out the threshold values for both algorithms. When the number of variables N is large, the threshold values tend to zero, so generally speaking PRW does not work on Model RB.