Determining the Basis for Performance Variations in CSP Heuristics

This paper develops the idea that variable ordering heuristics can be classified on the basis of a small number of distinguishable actions, and that while specific heuristics may be classified differently depending on the problem type, the basic actions that determine their classification are the same. Previous work demonstrated two basic categories of heuristics, and that problems in an apparently homogeneous problem set differ in their amenability to heuristics of different types. The present paper shows that these heuristic actions, which may be described as building up contention and propagating effects, have distinct values for descriptive measures such as depth of failure and the depth at which a problem becomes tractable, that reflect differences in the rapidity of their effects with respect to search depth. Heuristics behave similarly with respect to their basic actions across a wide range of propagation, from simple backtracking to maintained arc consistency. The propagation- of-effects type of action is closely related to the "simplification hypothesis" of Hooker and Vinay. This work contributes to the goals of explaining heuristic performance and putting heuristic selection on a rational basis.