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COCO
2005
Springer

Hardness of Max 3SAT with No Mixed Clauses

13 years 9 months ago
Hardness of Max 3SAT with No Mixed Clauses
We study the complexity of approximating Max NME3SAT, a variant of Max 3SAT when the instances are guaranteed to not have any mixed clauses, i.e., every clause has either all its literals unnegated or all of them negated. This is a natural special case of Max 3SAT introduced in [7], where the question of whether this variant can be approximated within a factor better than 7/8 was also posed. We prove that it is NP-hard to approximate Max NME3SAT within a factor of 7/8 + ε for arbitrary ε > 0, and thus this variant is no easier to approximate than general Max 3SAT. The proof uses the technique of multilayered PCPs, introduced in [3], to avoid the technical requirement of folding of the proof tables. Circumventing this requirement means that the PCP verifier can use the bits it accesses without additional negations, and this leads to a hardness for Max 3SAT without any mixed clauses.
Venkatesan Guruswami, Subhash Khot
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where COCO
Authors Venkatesan Guruswami, Subhash Khot
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