TITLE:
Complexity Analysis of Mixed Constraint Satisfaction Problems
AUTHORS:
Xiaomei Shi
KEYWORDS:
Model RBmix, Tree-Like Resolution, Complexity, Hard Instances
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.7 No.4,
April
26,
2017
ABSTRACT: This paper analyzes the resolution complexity of a random CSP model named model RBmix, the instance of which is composed by constraints with different length. For model RBmix, the existence of phase transitions has been established and the threshold points have been located exactly. By encoding the random instances into CNF formulas, it is proved that almost all instances of model RBmix have no tree-like resolution proofs of less than exponential size. Thus the model RBmix can generate abundant hard instances in the threshold. This result is of great significance for algorithm testing and complexity analysis in NP-complete problems.