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- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Birkhäuser / Springer Basel AG
- Subject
- Mathematics; Mathematics, general; Computer Science, general
- ISSN
- 1661-8270
- eISSN
- 1661-8289
- DOI
- 10.1007/s11786-010-0036-3
- Publisher site
- See Article on Publisher Site
Abstract
In this work we propose and analyze a simple randomized algorithm for 3-SAT (i.e. an algorithm to find a satisfiable assignment for a Boolean formula in conjunctive normal form (CNF) having at most 3 literals in every clause). Given a k-CNF formula $${\phi}$$ on n variables, and $${\alpha \in \{0,1\}^n}$$ that satisfies $${\phi}$$ , a clause of $${\phi}$$ is critical if exactly one literal of that clause is satisfied under assignment α. Paturi et al. (Chicago J. Theor. Comput. Sci. 115, 1999) proposed a simple randomized algorithm (PPZ) for k-SAT for which success probability increases with the number of critical clauses (with respect to a fixed satisfiable solution of the input formula). Here, we first describe another simple randomized algorithm DEL which performs better if the number of critical clauses in input formula are less (with respect to a fixed satisfiable solution of the input formula). Subsequently, we combine these two simple algorithms such that the success probability of the combined algorithm is maximum of the success probabilities of PPZ and DEL on every input instance. We show that when the average number of clauses for a variable that appear as unique true literals in one or more critical clauses in $${\phi}$$ is between 1 and 2/(3 · log (3/2)), combined algorithm performs better than the PPZ algorithm.
Journal
Mathematics in Computer Science – Springer Journals
Published: Apr 16, 2010