Probabilistic analysis of two heuristics for the 3-satisfiability problem
SIAM Journal on Computing
Many hard examples for resolution
Journal of the ACM (JACM)
Information Sciences: an International Journal
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
A general upper bound for the satisfiability threshold of random r-SAT formulae
Journal of Algorithms
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Bounding the unsatisfiability threshold of random 3-SAT
Random Structures & Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Average Case Analysis of a Greedy Algorithm for the Minimum Hitting Set Problem
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
A new bound for an NP-hard subclass of 3-SAT using backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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This paper is concerned with an algorithm that provides short certificates of unsatisfiability with high probability when an input I is a random instance of 3-SAT. Rather than build a refutation DAG, the algorithm finds bounds on nI(true), the number of variables that must be set to true, and nI(false), the number that must be set to false, if all clauses of I are to be satisfied. If the sum nI(true) + nI(false) is greater than the number of variables in I then I must be unsatisfiable. Bounds on nI(true) and nI(false) may be found by throwing out all clauses except those having only negative or only positive literals and finding nI+(true) for the remaining positive clause set I+ and nI-(false) for the remaining negative clause set I-. These questions can alternatively be stated as 3-hitting set problems on I+ and I- separately. It is shown that a good enough approximation algorithm for 3-hitting set can determine useful bounds on nI(true) and nI(false) (high probability of success for large enough constant ratio of clauses to variables). Although a good enough algorithm seems evasive, one that comes fairly close is proposed and analyzed.