A Mini-bucket-based Scheme for Approximating Combinatorial Optimization Tasks: Preliminary Results

The paper addresses the problem of computing lower bounds on the optimal costs associated with each unary assignment of a value to a variable in combinatorial optimization problems. This problem is instrumental in a variety of domains, in particular in proba-bilistic reasoning. Our aim is to use such lower bounds as a look-ahead procedure guiding search algorithms for optimal solutions. In particular, such lower bounds can be used in look-ahead methods for dynamic variable and value selections strategies that detect and prune infeasible values. The paper applies the mini-bucket elimination scheme 3] to accomplish this task. We show that by applying the mini-bucket elimination just twice, up and down, along a bucket-tree ordering, we may get a linear speed up over a brute-force application of this approximation idea for that task. Such performance improvements are essential if we are planning to apply the scheme at every node in the search tree.