Abstract
The paper presents an algorithm called directional resolution, avariation on the original Davis-Putnam algorithm, and analyzes its worst-case behavior as a function of the topological structure of propositional theories. The concepts of induced width and diversity are shown to play a key role in bounding the complexity of the procedure. The importance of our analysis lies in highlighting structure-based tractable classes of satisfiability and in providing theoretical guarantees on the time and space complexity of the algorithm. Contrary to previous assessments, we show that for many theories directional resolution could be an effective procedure. Our empirical tests confirm theoretical prediction, showing that on problems with a special structure, namely k-tree embeddings (e.g. chains, (k,m)-trees), directional resolution greatly outperforms one of the most effective satisfiability algorithms known to date, the popular Davis-Putnam procedure. Furthermore, combining a bounded version of directional resolution with the Davis-Putnam procedure results in an algorithm superior to either components.