On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
New methods to color the vertices of a graph
Communications of the ACM
Radio Link Frequency Assignment
Constraints
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
Journal of Automated Reasoning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A backbone-search heuristic for efficient solving of hard 3-SAT formulae
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
CSCLP'04 Proceedings of the 2004 joint ERCIM/CoLOGNET international conference on Recent Advances in Constraints
Heavy-Tailed runtime distributions: heuristics, models and optimal refutations
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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Variable ordering heuristics have long been an important component of constraint satisfaction search algorithms. In this paper we study the behaviour of standard variable ordering heuristics when searching an insoluble (sub)problem. We employ the notion of an optimal refutation of an insoluble (sub)problem and describe an algorithm for obtaining it. We propose a novel approach to empirically looking at problem hardness and typical-case complexity by comparing optimal refutations with those generated by standard search heuristics. It is clear from our analysis that the standard variable orderings used to solve CSPs behave very differently on real-world problems than on random problems of comparable size. Our work introduces a potentially useful tool for analysing the causes of the heavy-tailed phenomenon observed in the runtime distributions of backtrack search procedures.