Abstract. While CNF propositional satisfiability (SAT) is a sub-class of the more general constraint satisfaction problem (CSP), conventional wisdom has it that some well-known CSP look-back techniques --including backjumping and learning --are of little use for SAT. We enhance the Tableau SAT algorithm of Crawford and Auton with look-back techniques and evaluate its performance on problems specifically designed to challenge it.The Random 3-SAT problem space has commonly been used to benchmark SAT algorithms because consistently difficult instances can be found near a region known as the phase transition. We modify Random 3-SAT in two ways which make instances even harder. First, we evaluate problems with structural regularities and find that CSP look-back techniques offer little advantage. Second, we evaluate problems in which a hard unsatisfiable instance of medium size is embedded in a larger instance, and we find the look-back enhancements to be indispensable. Without them, most instances are "exceptionally hard" --orders of magnitude harder than typical Random 3-SAT instances with the same surface characteristics.
We present a pattern-mining algorithm that scales roughly linearly in the number of maximal patterns embedded in a database irrespective of the length of the longest pattern. In comparison, previous algorithms based on Apriori scale exponentially with longest pattern length. Experiments on real data show that when the patterns are long, our algorithm is more efficient by an order of magnitude or more.
We present a pattern-mining algorithm that scales roughly linearly in the number of maximal patterns embedded in a database irrespective of the length of the longest pattern. In comparison, previous algorithms based on Apriori scale exponentially with longest pattern length. Experiments on real data show that when the patterns are long, our algorithm is more efficient by an order of magnitude or more.
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