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Optimization and probabilistic satisfiability on nested and co-nested formulas

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  • Daniele Pretolani

Abstract

Nested and co-nested formulas are two classes of CNF instances that can be characterized in terms of outerplanar graphs. For these classes, linear time algorithms are known for SAT and (unweighted) Max-SAT. In this paper we devise linear time algorithms for a general optimization version of SAT. Moreover, we show that a general probabilistic version of SAT reduces to solving a system of linear inequalities where the number of variables and constraints is linear in the size of the formula. Copyright Springer Science+Business Media, LLC 2011

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  • Daniele Pretolani, 2011. "Optimization and probabilistic satisfiability on nested and co-nested formulas," Annals of Operations Research, Springer, vol. 188(1), pages 371-387, August.
    • Handle: RePEc:spr:annopr:v:188:y:2011:i:1:p:371-387:10.1007/s10479-008-0502-3
    DOI: 10.1007/s10479-008-0502-3
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    References listed on IDEAS

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    1. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
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