An Instance of Adaptive Constraint Propagation

Constraint propagation algorithms vary in the strength of propagation they apply. This paper investigates a simple connguration for adaptive propagation { the process of varying the strength of propagation to reeect the dynamics of search. We focus on two propagation methods, Arc Consistency (AC) and Forward Checking (FC). AC-based algorithms apply a stronger form of propagation than FC-based algorithms; they invest greater computational eeort to detect inconsistent values earlier. The relative payoo of maintaining AC during search as against FC may vary for diierent constraints and for diierent intermediate search states. We present a scheme for Adaptive Arc Propagation (AAP) that allows the exible combination of the two methods. Meta-level reasoning and heuristics are used to dynamically distribute propagation eeort between the two. One instance of AAP, Anti-Functional Reduction (AFR), is described in detail here. AFR achieves precisely the same propagation as a pure AC algorithm while signiicantly improving its average performance. The strategy is to gradually reduce the scope of AC propagation during backtrack search to exclude those arcs that may be subsequently handled as eeectively by FC. Experimental results connrm the power of AFR and the validity of adaptive propagation in general.