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An algorithm for the sat problem for formulae of linear lengthPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2005 (English)In: Algorithms – ESA 2005: 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005., 2005, 107 -118 p.Conference paper (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

2005. 107 -118 p.
##### Series

, Lecture Notes in Computer Science, ISSN 0302-9743 (Print) 1611-3349 (Online) ; 3669
##### National Category

Engineering and Technology
##### Identifiers

URN: urn:nbn:se:liu:diva-14398DOI: 10.1007/11561071ISBN: 978-3-540-29118-3OAI: oai:DiVA.org:liu-14398DiVA: diva2:23419
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Available from: 2007-04-16 Created: 2007-04-16 Last updated: 2009-06-08
##### In thesis

We present an algorithm that decides the satisfiability of a CNF formula where every variable occurs at most *k* times in time for some *c* (that is, *O*(*α*^{N}) with for every fixed *k*). For *k* ≤ 4, the results coincide with an earlier paper where we achieved running times of *O*(2^{0.1736N}) for *k* = 3 and *O*(2^{0.3472N}) for *k* = 4 (for *k* ≤ 2, the problem is solvable in polynomial time). For *k*>4, these results are the best yet, with running times of *O*(2^{0.4629N}) for *k* = 5 and *O*(2^{0.5408N}) for *k* = 6. As a consequence of this, the same algorithm is shown to run in time *O*(2^{0.0926L}) for a formula of length (total number of literals) *L*. The previously best bound in terms of *L* is *O*(2^{0.1030L}). Our bound is also the best upper bound for an exact algorithm for a 3sat formula with up to six occurrences per variable, and a 4sat formula with up to eight occurrences per variable.

1. Algorithms, measures and upper bounds for satisfiability and related problems$(function(){PrimeFaces.cw("OverlayPanel","overlay23420",{id:"formSmash:j_idt706:0:j_idt710",widgetVar:"overlay23420",target:"formSmash:j_idt706:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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