(2 + epsilon)-Sat Is NP-hard
2014 (English)In: Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, 2014, 1-10 p.Conference paper (Refereed)
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.
Place, publisher, year, edition, pages
2014. 1-10 p.
, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, ISSN 0272-5428 ; 6978984
complexity dichotomy, Constraint satisfaction, discrepancy, polymorphisms, probabilistically checkable proofs, promise problems
IdentifiersURN: urn:nbn:se:kth:diva-167553DOI: 10.1109/FOCS.2014.9ISI: 000366324300001ScopusID: 2-s2.0-84919962415ISBN: 9781479965175OAI: oai:DiVA.org:kth-167553DiVA: diva2:818216
55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014, 18 October 2014 through 21 October 2014
QC 201506082015-06-082015-05-222016-01-07Bibliographically approved