TITLE:
Sharp Thresholds for a Random Constraint Satisfaction Problem
AUTHORS:
Ya'nan Liu
KEYWORDS:
d-p-RB Model, Phase Transition, Domain Size, Constraint Tightness, Second Moment Method
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.7 No.10,
October
31,
2017
ABSTRACT: The phenomenon of phase transition in constraint satisfaction problems (CSPs) plays a crucial role in the field of artificial intelligence and computational complexity theory. In this paper, we propose a new random CSP called d-p-RB model, which is a generalization of RB model on domain size d and constraint tightness p. In this model, the variable domain size dΕ [ nα, nny], and all constraints are uniformly divided into several groups with different constraint tightness p. It is proved by the second moment method that the d-p-RB model undergoes phase transition from a region where almost all instances are satisfiable to a region where almost all instances are unsatisfiable as the control parameter increases. Moreover, the threshold value at which the phase transition occurs is located exactly.