References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

(2 + epsilon)-Sat Is NP-hardPrimeFaces.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}); 2014 (English)In: Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2014, 1-10 p.Conference paper (Refereed)
##### Abstract [en]

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

2014. 1-10 p.
##### Series

, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, ISSN 0272-5428 ; 6978984
##### Keyword [en]

complexity dichotomy, Constraint satisfaction, discrepancy, polymorphisms, probabilistically checkable proofs, promise problems
##### National Category

Computer Science
##### Identifiers

URN: urn:nbn:se:kth:diva-167553DOI: 10.1109/FOCS.2014.9ISI: 000366324300001ScopusID: 2-s2.0-84919962415ISBN: 9781479965175OAI: oai:DiVA.org:kth-167553DiVA: diva2:818216
##### Conference

55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014, 18 October 2014 through 21 October 2014
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Note

We prove the following hardness result for anatural promise variant of the classical CNF-satisfiabilityproblem: Given a CNF-formula where each clause has widthw and the guarantee that there exists an assignment satisfyingat least g = [w/2]-1 literals in each clause, it is NP-hard tofind a satisfying assignment to the formula (that sets at leastone literal to true in each clause). On the other hand, when g = [w/2], it is easy to find a satisfying assignment via simplegeneralizations of the algorithms for 2-SAT. Viewing 2-SAT σ P as easiness of SAT when 1-in-2 literals are true in every clause, and NP-hardness of 3-SAT as intractability of SAT when 1-in-3 literals are true, our resultshows, for any fixed &epsi; > 0, the hardness of finding a satisfyingassignment to instances of '(2 + &epsi;)-SAT' where the density ofsatisfied literals in each clause is promised to exceed 1/(2+ε). We also strengthen the results to prove that given a (2k + 1)-uniform hypergraph that can be 2-colored such that each edgehas perfect balance (at most k + 1 vertices of either color), itis NP-hard to find a 2-coloring that avoids a monochromaticedge. In other words, a set system with discrepancy 1 is hard todistinguish from a set system with worst possible discrepancy.

QC 20150608

Available from: 2015-06-08 Created: 2015-05-22 Last updated: 2016-01-07Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});