Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
(2 + epsilon)-Sat Is NP-hard
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0001-8217-0158
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-5379-345X
2014 (English)In: Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2014, 1-10 p.Conference paper, Published paper (Refereed)
Abstract [en]

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 ε > 0, the hardness of finding a satisfyingassignment to instances of '(2 + ε)-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.

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: 000366324300001Scopus ID: 2-s2.0-84919962415ISBN: 9781479965175 (print)OAI: 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
Note

QC 20150608

Available from: 2015-06-08 Created: 2015-05-22 Last updated: 2016-01-07Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Authority records BETA

Austrin, PerHåstad, Johan

Search in DiVA

By author/editor
Austrin, PerHåstad, Johan
By organisation
Theoretical Computer Science, TCS
Computer Science

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 73 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf