Arc and path consistence revisited
Artificial Intelligence
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Constraint satisfaction algorithms
Computational Intelligence
The hardest constraint problems: a double phase transition
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
Journal of Automated Reasoning
Resolution versus Search: Two Strategies for SAT
Journal of Automated Reasoning
Contradicting Conventional Wisdom in Constraint Satisfaction
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
A Bayesian Approach to Tackling Hard Computational Problems
UAI '01 Proceedings of the 17th Conference in Uncertainty in 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
Eighteenth national conference on Artificial intelligence
Constraint Processing
Stochastic Local Search: Foundations & Applications
Stochastic Local Search: Foundations & Applications
Exact phase transitions in random constraint satisfaction problems
Journal of Artificial Intelligence Research
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Sparse constraint graphs and exceptionally hard problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Summarizing CSP hardness with continuous probability distributions
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Fast estimation of first-order clause coverage through randomization and maximum likelihood
Proceedings of the 25th international conference on Machine learning
A Restarted Strategy for Efficient Subsumption Testing
Fundamenta Informaticae - Progress on Multi-Relational Data Mining
A generative power-law search tree model
Computers and Operations Research
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
AAAI'08 Proceedings of the 23rd 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
Random instances of W[2]-complete problems: thresholds, complexity, and algorithms
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Combining Constraint Programming and Local Search for Job-Shop Scheduling
INFORMS Journal on Computing
Understanding the behavior of Solution-Guided Search for job-shop scheduling
Journal of Scheduling
Impact of censored sampling on the performance of restart strategies
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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
A Restarted Strategy for Efficient Subsumption Testing
Fundamenta Informaticae - Progress on Multi-Relational Data Mining
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Much progress has been made in terms of boosting the effectiveness of backtrack style search methods. In addition, during the last decade, a much better understanding of problem hardness, typical case complexity, and backtrack search behavior has been obtained. One example of a recent insight into backtrack search concerns so-called heavy-tailed behavior in randomized versions of backtrack search. Such heavy-tails explain the large variance in runtime often observed in practice. However, heavy-tailed behavior does certainly not occur on all instances. This has led to a need for a more precise characterization of when heavy-tailedness does and when it does not occur in backtrack search. In this paper, we provide such a characterization. We identify different statistical regimes of the tail of the runtime distributions of randomized backtrack search methods and show how they are correlated with the "sophistication" of the search procedure combined with the inherent hardness of the instances. We also show that the runtime distribution regime is highly correlated with the distribution of the depth of inconsistent subtrees discovered during the search. In particular, we show that an exponential distribution of the depth of inconsistent subtrees combined with a search space that grows exponentially with the depth of the inconsistent subtrees implies heavy-tailed behavior.