A sharp threshold in proof complexity
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
Backdoor Sets for DLL Subsolvers
Journal of Automated Reasoning
Parameterized Proof Complexity
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Parameterized complexity of constraint satisfaction problems
Computational Complexity
Generating hard satisfiable formulas by hiding solutions deceptively
Journal of Artificial Intelligence Research
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
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
Parameterized Complexity
Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability
Artificial Intelligence
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The study of random instances of NP complete and coNP complete problems has had much impact on our understanding of the nature of hard problems. In this work, we initiate an effort to extend this line of research to random instances of intractable parameterized problems. We propose random models for a representative intractable parameterized problem, the weighted d-CNF satisfiability, and its generalization to the constraint satisfaction problem. The exact threshold for the phase transition of the proposed models is determined. Lower bounds on the time complexity of variants of the DPLL algorithm for these parameterized problems are also established. In particularly, we show that random instances of the weighted 2-CNF satisfiability, already an intractable parameterized problem, are typically easy in both of the satisfiable and unsatisfiable regions by exploiting an interesting connection between the unsatisfiability of a weighted 2-CNF formula and the existence of a Hamiltonian-cycle-like global structure.