Balanced max 2-sat might not be the hardest

We show that, assuming the Unique Games Conjecture, it is NPhard to approximate MAX 2-SAT within LLZ + , where 0.9401 < LLZ < 0.9402 is the believed approximation ratio of the algorithm of Lewin, Livnat and Zwick [28]. This result is surprising considering the fact that balanced instances of MAX 2-SAT, 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%. Categories and Subject Descriptors F.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General Terms Theory Keywords Max 2-Sat, Unique Games Conjecture, Inapproximability

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Per Austrin
• Keywords: Algorithms, Believed Approximation Ratio, Problems General Terms, STOC 2007, Unique Games