Spectra, Euclidean representations and clusterings of hypergraphs
Discrete Mathematics
Approximability of maximum splitting of k-sets and some other Apx-complete problems
Information Processing Letters
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
The phase transition in 1-in-k SAT and NAE 3-SAT
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximating minimum unsatisfiability of linear equations
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Recognizing More Unsatisfiable Random 3-SAT Instances Efficiently
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Combinatorics, Probability and Computing
Max k-cut and approximating the chromatic number of random graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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It is known that random k-Sat instances with at least cn random clauses where c = ck is a suitable constant are unsatisfiable with high probability. These results are obtained by estimating the expected number of satisfying assignments and thus do not provide us with an efficient algorithm. Concerning efficient algorithms it is only known that formulas with n驴 驴nk/2 clauses with k literals over n underlying variables can be efficiently certified as unsatisfiable. The present paper is the result of trying to lower the preceding bound.We obtain better bounds for some specialized satisfiability problems.