Years and Authors of Summarized Original Work
2005; Paturi, Pudlák, Saks, Zane
Problem Definition
Determination of the complexity of k-CNF satisfiability is a celebrated open problem: given a Boolean formula in conjunctive normal form with at most k literals per clause, find an assignment to the variables that satisfies each of the clauses or declare none exists. It is well known that the decision problem of k-CNF satisfiability is NP-complete for k ≥ 3. This entry is concerned with algorithms that significantly improve the worst-case running time of the naive exhaustive search algorithm, which is poly(n)2n for a formula on n variables. Monien and Speckenmeyer [8] gave the first real improvement by giving a simple algorithm whose running time is \(O(2_{k}^{(1-\upvarepsilon )n})\), with \(\upvarepsilon _{k}> 0\) for all k. In a sequence of results [1, 3, 5–7, 9–12], algorithms with increasingly better running times (larger values of \(\upvarepsilon _{k}\)) have been proposed and...
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Paturi, R., Pudlák, P., Saks, M., Zane, F. (2016). Backtracking Based k-SAT Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_45
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