A constraint-based approach to narrow search trees for satisfiability
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
The backdoor key: a path to understanding problem hardness
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Evolving combinatorial problem instances that are difficult to solve
Evolutionary Computation
Finding critical backbone structures with genetic algorithms
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Exploiting automatically inferred constraint-models for building identification in satellite imagery
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
SAT graph-based representation: A new perspective
Journal of Algorithms
Probabilistically Estimating Backbones and Variable Bias: Experimental Overview
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A New Empirical Study of Weak Backdoors
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A generative power-law search tree model
Computers and Operations Research
Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
Backdoors in the Context of Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
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
Using expectation maximization to find likely assignments for solving CSP's
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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
Backdoor sets of quantified boolean formulas
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Reformulating CSPs for scalability with application to geospatial reasoning
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
From horn strong backdoor sets to ordered strong backdoor sets
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
Efficient generic search heuristics within the EMBP framework
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
On Computing Backbones of Propositional Theories
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Benefits of a population: five mechanisms that advantage population-based algorithms
IEEE Transactions on Evolutionary Computation
Propelling SAT and SAT-based BMC using careset
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Finding small backdoors in SAT instances
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
Generating highly balanced sudoku problems as hard problems
Journal of Heuristics
Is computational complexity a barrier to manipulation?
Annals of Mathematics and Artificial Intelligence
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
From approximate clausal reasoning to problem hardness
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
A multilevel algorithm for large unconstrained binary quadratic optimization
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Reasoning over biological networks using maximum satisfiability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Change propagation due to uncertainty change
FASE'13 Proceedings of the 16th international conference on Fundamental Approaches to Software Engineering
Backbone guided tabu search for solving the UBQP problem
Journal of Heuristics
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
On computing minimal correction subsets
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
A generalization of SAT and #SAT for robust policy evaluation
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Crowdsourcing backdoor identification for combinatorial optimization
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We study the backbone and the backdoors of propositional satisfiability problems. We make a number of theoretical, algorithmic and experimental contributions. From a theoretical perspective, we prove that backbones are hard even to approximate. From an algorithmic perspective, we present a number of different procedures for computing backdoors. From an empirical perspective. we study the correlation between being in the backbone and in a backdoor. Experiments show that there tends to be very little overlap between backbones and backdoors. We also study problem hardness for the Davis Putnam procedure. Problem hardness appears to be correlated with the size of strong backdoors, and weakly correlated with the size of the backbone, but does not appear to be correlated to the size of weak backdoors nor their number. Finally, to isolate the effect of backdoors, we look at problems with no backbone.