A general model and thresholds for random constraint satisfaction problems

In this paper, we study the relation among the parameters in their most general setting that define a large class of random CSP models d-k-CSP where d is the domain size and k is the length of the constraint scopes. The model d-k-CSP unifies several related models such as the model RB and the model k-CSR We prove that the model d-k-CSP exhibits exact phase transitions if klnd increases no slower than the logarithm of the number of variables. A series of experimental studies with interesting observations are carried out to illustrate the solubility phase transition and the hardness of instances around phase transitions. Crown Copyright (C) 2012 Published by Elsevier B.V. All rights reserved.