The Curse and Blessing of Not-All-Equal in k-Satisfiability

09/12/2018

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by   Sixue Liu, et al.

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We study upper bounds for the running time of algorithms for NAE-k-SAT and MAX-NAE-k-SAT approximation, as functions of k, the number of variables n and the performance ratio δ. For the first time, deterministic NAE-k-SAT algorithm is faster than the best k-SAT algorithm. The analysis relies on Linear Programming. However we do not know such improvement for randomized algorithms. As for approximation algorithms, we show that a number of MAX-k-SAT algorithms do not apply to MAX-NAE-k-SAT, including the current best one. We present a better MAX-NAE-k-SAT approximation algorithm, which is even faster than the best MAX-k-SAT approximation algorithm in a wide range of δ when k = 3. We also provide a tighter analysis on an existing MAX-k-SAT approximation algorithm, and generalize it for MAX-NAE-k-SAT, which is currently the best for all k > 4.