Dynamic Bundling: Less Effort for More Solutions

Bundling of the values of variables in a Constraint Satisfaction Problem (CSP) as the search proceeds is an abstraction mechanism that yields a compact representation of the solution space. We have previously established that, in spite of the effort of recomputing the bundles, dynamic bundling is never less effective than static bundling and non-bundling search strategies. Objections were raised that bundling mechanisms (whether static or dynamic) are too costly and not worthwhile when one is not seeking all solutions to the CSP. In this paper, we dispel these doubts and empirically show that (1) dynamic bundling remains superior in this context, (2) it does not require a full lookahead strategy, and (3) it dramatically reduces the cost of solving problems at the phase transition while yielding a bundle of multiple, robust solutions.