A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
The scaling window of the 2-SAT transition
Random Structures & Algorithms
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Models and thresholds for random constraint satisfaction problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Coloring Bipartite Hypergraphs
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
The threshold for random k-SAT is 2k (ln 2 - O(k))
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Solving random satisfiable 3CNF formulas in expected polynomial time
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Backdoor Sets for DLL Subsolvers
Journal of Automated Reasoning
Invitation to data reduction and problem kernelization
ACM SIGACT News
Random constraint satisfaction: Easy generation of hard (satisfiable) instances
Artificial Intelligence
Improved algorithms for path, matching, and packing problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
Algorithmica - Parameterized and Exact Algorithms
The parameterized complexity of global constraints
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
Hiding satisfying assignments: two are better than one
Journal of Artificial Intelligence Research
Generating hard satisfiable formulas by hiding solutions deceptively
Journal of Artificial Intelligence Research
Consistency and random constraint satisfaction models
Journal of Artificial Intelligence Research
Phase transition for random quantified XOR-formulas
Journal of Artificial Intelligence Research
An analysis of phase transition in NK landscapes
Journal of Artificial Intelligence Research
Backbone guided local search for maximum satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Exact algorithms for cluster editing: evaluation and experiments
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Parameterized bounded-depth Frege is not optimal
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Parameterized Bounded-Depth Frege Is not Optimal
ACM Transactions on Computation Theory (TOCT)
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
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Data reduction is a key technique in the study of fixed parameter algorithms. In the AI literature, pruning techniques based on simple and efficient-to-implement reduction rules also play a crucial role in the success of many industrial-strength solvers. Understanding the effectiveness and the applicability of data reduction as a technique for designing heuristics for intractable problems has been one of the main motivations in studying the phase transition of randomly-generated instances of NP-complete problems. In this paper, we take the initiative to study the power of data reductions in the context of random instances of a generic intractable parameterized problem, the weighted d-CNF satisfiability problem. We propose a non-trivial random model for the problem and study the probabilistic behavior of the random instances from the model. We design an algorithm based on data reduction and other algorithmic techniques and prove that the algorithm solves the random instances with high probability and in fixed-parameter polynomial time O(d^knm) where n is the number of variables, m is the number of clauses, and k is the fixed parameter. We establish the exact threshold of the phase transition of the solution probability and show that in some region of the problem space, unsatisfiable random instances of the problem have parametric resolution proof of fixed-parameter polynomial size. Also discussed is a more general random model and the generalization of the results to the model.