Variable and term removal from Boolean formulae
Discrete Applied Mathematics
Approximation algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
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
On approximating minimum vertex cover for graphs with perfect matching
Theoretical Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Backdoor Sets for DLL Subsolvers
Journal of Automated Reasoning
Solving #SAT using vertex covers
Acta Informatica
The backdoor key: a path to understanding problem hardness
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Backdoor sets of quantified boolean formulas
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Algorithms for propositional model counting
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Parameterized Complexity
Backdoors in the Context of Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Finding small backdoors in SAT instances
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Backdoors to tractable answer-set programming
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Existential closures for knowledge compilation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The Multivariate Algorithmic Revolution and Beyond
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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The surprisingly good performance of modem satisfiability (SAT) solvers is usually explained by the existence of a certain "hidden structure" in real-world instances. We introduce the notion of backdoor trees as an indicator for the presence of a hidden structure. Backdoor trees refine the notion of strong backdoor sets, taking into account the relationship between backdoor variables. We present theoretical and empirical results. Our theoretical results are concerned with the computational complexity of detecting small backdoor trees. With our empirical results we compare the size of backdoor trees against the size of backdoor sets for real-world SAT instances and random 3SAT instances of various density. The results indicate that backdoor trees amplify the properties that have been observed for backdoor sets.