Automatic discovery and exploitation of promising subproblems for tabulation

Abstract

The performance of a constraint model can often be improved by converting a subproblem into a single table constraint. In this paper we study heuristics for identifying promising subproblems. We propose a small set of heuristics to identify common cases such as expressions that will propagate weakly. The process of discovering promising subproblems and tabulating them is entirely automated in the tool Savile Row. A cache is implemented to avoid tabulating equivalent subproblems many times. We give a simple algorithm to generate table constraints directly from a constraint expression in Savile Row. We demonstrate good performance on the benchmark problems used in earlier work on tabulation, and also for several new problem classes.