Better Approximation Algorithms and Tighter Analysis for Set Splitting and Not-All-Equal Sat

We construct new approximation algorithms for Max Set Splitting and Max Not-All-Equal Sat, which when combined with existing algorithms give the best approximation results so far for these problems. Furthermore, when analyzing our combination of approximation algorithms, we introduce a novel technique, which improves the analysis of the performance ratio of such algorithms. In contrast with previous techniques we use a linear program to nd an upper bound on the performance ratio. This linear program can also be used to see which of the contributing algorithms it is possible to exclude from the combined algorithm without aaecting its performance ratio.