Estimating Problem Metrics for SAT Clause Weighting Local Search

Considerable progress has recently been made in using clause weighting algorithms to solve SAT benchmark problems. While these algorithms have outperformed earlier stochastic techniques on many larger problems, this improvement has generally required extra, problem specific, parameters which have to be fine tuned to problem domains to obtain optimal run-time performance. In a previous paper, the use of parameters, specifically in relation to the DLM clause weighting algorithm, was examined to identify underlying features in clause weighting that could be used to eliminate or predict workable parameter settings. A simplified clause weighting algorithm (Maxage), based on DLM, was proposed that reduced the parameters to a single parameter. Also, in a previous paper, the structure of SAT problems was investigated and a measure developed which allowed the classification of SAT problems into random, loosely structured or compactly structured. This paper extends this work by investigating the behaviour of Maxage with regard to the structural characteristics of SAT problems. The underlying motivation for this study is the development of an adaptive, parameterless clause weighting algorithm.