Balanced max 2-sat might not be the hardest

Authors:
Per Austrin
Affiliations:
KTH - Royal Institute of Technology, Stockholm, Sweden
Venue:
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Year:
2007

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Abstract

We show that, assuming the Unique Games Conjecture, it is NP-hard to approximate MAX2SAT within αLLZ-+ε, where 0.9401 LLZ- This result is surprising considering the fact that balanced instances of MAX2SAT, i.e., instances where each variable occurs positively and negatively equally often, can be approximated within 0.9439. In particular, instances in which roughly 68% of the literals are unnegated variables and 32% are negated appear less amenable to approximation than instances where the ratio is 50% - 50%.