Variable Ordering Heuristics Show Promise

Abstract

Promise is the ability to make choices that lead to a solution when one exists. The traditional intuition behind variable ordering heuristics is Haralick and Elliott’s fail-first principle: choose the variable such that assigning it is most likely to lead to a domain wipe-out (in AIJ 14, 1980). In contrast, the standard belief about value ordering heuristics is based on Geelen’s discussion (in ECAI’92): choose a value that is most likely to participate in a solution. It is not clear a priori that changes in variable ordering change the likelihood of finding a solution in a way that will affect overall performance significantly. In this paper we show that promise does have a meaning for variable ordering heuristics and that the level of promise of a variable ordering heuristic can be measured. In addition, we show that the promise of different variable ordering heuristics is different and that the level of promise of a variable ordering heuristic correlates with search cost for problems with many solutions.

This work has received support from Science Foundation Ireland under Grant 00/PI.1/C075 and ILOG, SA.