Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
The hardest constraint problems: a double phase transition
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
New methods to color the vertices of a graph
Communications of the ACM
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
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Formal Models of Heavy-Tailed Behavior in Combinatorial Search
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
In Search of Exceptionally Difficult Constraint Satisfaction Problems
Constraint Processing, Selected Papers
Backjump-Based Techniques versus Conflict-Directed Heuristics
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Sparse constraint graphs and exceptionally hard problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Optimal refutations for constraint satisfaction problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Value ordering for quantified CSPs
Constraints
A generative power-law search tree model
Computers and Operations Research
The impact of balancing on problem hardness in a highly structured domain
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Solution-guided multi-point constructive search for job shop scheduling
Journal of Artificial Intelligence Research
Fitness-distance correlation and solution-guided multi-point constructive search for CSPs
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism
Journal of Experimental Algorithmics (JEA)
Failure analysis in backtrack search for constraint satisfaction
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Heavy-Tailed runtime distributions: heuristics, models and optimal refutations
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Counting-based search: branching heuristics for constraint satisfaction problems
Journal of Artificial Intelligence Research
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The heavy-tailed phenomenon that characterises the runtime distributions of backtrack search procedures has received considerable attention over the past few years. Some have conjectured that heavy-tailed behaviour is largely due to the characteristics of the algorithm used. Others have conjectured that problem structure is a significant contributor. In this paper we attempt to explore the former hypothesis, namely we study how variable and value ordering heuristics impact the heavy-tailedness of runtime distributions of backtrack search procedures. We demonstrate that heavy-tailed behaviour can be eliminated from particular classes of random problems by carefully selecting the search heuristics, even when using chronological backtrack search. We also show that combinations of good search heuristics can eliminate heavy tails from quasigroups with holes of order 10 and 20, and give some insights into why this is the case. These results motivate a more detailed analysis of the effects that variable and value orderings can have on heavy-tailedness. We show how combinations of variable and value ordering heuristics can result in a runtime distribution being inherently heavy-tailed. Specifically, we show that even if we were to use an oracle to refute insoluble subtrees optimally, for some combinations of heuristics we would still observe heavy-tailed behaviour. Finally, we study the distributions of refutation sizes found using different combinations of heuristics and gain some further insights into what characteristics tend to give rise to heavy-tailed behaviour.