Value Ordering for Finding All Solutions: Interactions with Adaptive Variable Ordering

We consider the impact of value ordering heuristics on the search effort required to find all solutions, or proving none exist, to a constraint satisfaction problem in k-way branching search. We show that when the variable ordering heuristic is adaptive, the order in which the values are assigned to variables can make a significant difference in all measures of search effort. We study in depth an open issue regarding the relative merit of traditional value heuristics, and their complements, when searching for all solutions. We also introduce a lazy version of k-way branching and study the effect of value orderings on finding all solutions when it is used. This paper motivates a new and fruitful line of research in the study of value ordering heuristics for proving unsatisfiability.