Boosting Search with Variable Elimination

Abstract

Variable elimination is the basic step of Adaptive Consistency [4]. It transforms the problem into an equivalent one, having one less variable. Unfortunately, there are many classes of problems for which it is infeasible, due to its exponential space and time complexity. However, by restricting variable elimination so that only low arity constraints are processed and recorded, it can be effectively combined with search, because the elimination of variables, reduces the search tree size.

In this paper we introduce VarElimSearch(S,k), a hybrid meta-algorithm that combines search and variable elimination. The parameter S names the particular search procedure and k controls the tradeoff between the two strategies. The algorithm is space exponential in k. Regarding time, we show that its complexity is bounded by k and a structural parameter from the constraint graph. We also provide experimental evidence that the hybrid algorithm can outperform state-of-the-art algorithms in binary sparse problems. Experiments cover the tasks of finding one solution and the best solution (Max-CSP). Specially in the Max-CSP case, the advantage of our approach can be overwhelming.

This work was carried out while the author was visiting the University of California at Irvine with grant from Generalitat de Catalunya. The author is thankful to Rina Dechter for many useful comments and suggestions on previous versions of this paper. This research is partially funded by the Spanish CICYT under the project TAP1999-1086-C03-03 and by the NSF under grant IIS-9610015.