Who are the variables in your neighbourhood

Dynamic reordering techniques have had considerable success in reducing the impact of the initial variable order on the size of decision diagrams. Sifting, in particular, has emerged as a very good compromise between low CPU time requirements and high quality of results. Sifting, however, has the absolute position of a variable as the primary objective, and only considers the relative positions of groups of variables indirectly. In this paper we propose an extension to sifting that may move groups of variables simultaneously to produce better results. Variables are aggregated by checking whether they have a strong affinity to their neighbors. (Hence the title.) Our experiments show an average improvement in size of 11%. This improvement, coupled with the greater robustness of the algorithm, more than offsets the modest increase in CPU time that is sometimes incurred.