Mini-bucket Elimination with Bucket Propagation

Many important combinatorial optimization problems can be expressed as constraint satisfaction problems with soft constraints. When problems are too difficult to be solved exactly, approximation methods become the best option. Mini-bucket Elimination (MBE) is a well known approximation method for combinatorial optimization problems. It has a control parameter z that allow us to trade time and space for accuracy. In practice, it is the space and not the time that limits the execution with high values of z. In this paper we introduce a new propagation phase that MBE should execute at each bucket. The purpose of this propagation is to jointly process as much information as possible. As a consequence, the undesirable lose of accuracy caused by MBE when splitting functions into different mini-buckets is minimized. We demonstrate our approach in scheduling, combinatorial auction and max-clique problems, where the resulting algorithm MBE gives important percentage increments of the lower bound (typically 50% and up to 1566%) with only doubling the cpu time.