A sufficient condition for backtrack-bounded search
Journal of the ACM (JACM)
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Detecting embedded Horn structure in propositional logic
Information Processing Letters
On the minimality and global consistency of row-convex constraint networks
Journal of the ACM (JACM)
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
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
Formal Models of Heavy-Tailed Behavior in Combinatorial Search
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint Processing
Formal methods for the validation of automotive product configuration data
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Hidden Structure in Unsatisfiable Random 3-SAT: An Empirical Study
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Backdoor Sets for DLL Subsolvers
Journal of Automated Reasoning
Computing Horn Strong Backdoor Sets Thanks to Local Search
ICTAI '06 Proceedings of the 18th IEEE International Conference on Tools with Artificial Intelligence
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
An efficient arc consistency algorithm for a class of CSP problems
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Constraint satisfaction with bounded treewidth revisited
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Exploiting weak dependencies in tree-based search
Proceedings of the 2009 ACM symposium on Applied Computing
Backdoors to Combinatorial Optimization: Feasibility and Optimality
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Backdoors in the Context of Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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
Computation of renameable Horn backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Learning cluster-based structure to solve constraint satisfaction problems
Annals of Mathematics and Artificial Intelligence
Finding small backdoors in SAT instances
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
The Multivariate Algorithmic Revolution and Beyond
Strong backdoors to nested satisfiability
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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There has been considerable interest in the identification of structural properties of combinatorial problems that lead to efficient algorithms for solving them. Some of these properties are "easily" identifiable, while others are of interest because they capture key aspects of state-of-the-art constraint solvers. In particular, it was recently shown that the problem of identifying a strong Horn- or 2CNF-backdoor can be solved by exploiting equivalence with deletion backdoors, and is NP-complete. We prove that strong backdoor identification becomes harder than NP (unless NP=coNP) as soon as the inconsequential sounding feature of empty clause detection (present in all modern SAT solvers) is added. More interestingly, in practice such a feature as well as polynomial time constraint propagation mechanisms often lead to much smaller backdoor sets. In fact, despite the worst-case complexity results for strong backdoor detection, we show that Satz-Rand is remarkably good at finding small strong backdoors on a range of experimental domains. Our results suggest that structural notions explored for designing efficient algorithms for combinatorial problems should capture both statically and dynamically identifiable properties.