Optimal implementation of watched literals and more general techniques

Abstract

I prove that an implementation technique for scanning lists in backtracking search algorithms is optimal. The result applies to a simple general framework, which I present: applications include watched literal unit propagation in SAT and a number of examples in constraint satisfaction. Techniques like watched literals are known to be highly space efficient and effective in practice. When implemented in the 'circular' approach described here, these techniques also have optimal run time per branch in big-O terms when amortized across a search tree. This also applies when multiple list elements must be found. The constant factor overhead of the worst case is only 2. Replacing the existing non-optimal implementation of unit propagation in MiniSat speeds up propagation by 29%, though this is not enough to improve overall run time significantly.