On implementation choices for iterative improvement partitioning algorithms

Iterative improvement partitioning algorithms such as those due to Fiduccia and Mattheyses (1982) and Krishnamurthy (1984) exploit an efficient gain bucket data structure in selecting modules that are moved from one partition to the other. In this paper, we investigate three gain bucket implementations and their effect on the performance of the Fiduccia-Mattheyses partitioning algorithm. Surprisingly, selection from gain buckets maintained as Last-In-First-Out (LIFO) stacks leads to significantly better results than selection from gain buckets maintained randomly or as First-In-First-Out (FIFO) queues. Our experiments show that LIFO buckets result in a 35% improvement over random buckets and a 42% improvement over FIFO buckets. Furthermore, eliminating randomization from the bucket selection is of greater benefit to Fiduccia-Mattheyses performance than adding the Krishnamurthy gain vector. By combining insights from the LIFO gain buckets with those of Krishnamurthy's original work, a new higher-level gain formulation is proposed. This alternative formulation results in a further 16% reduction in the average cut cost when compared directly to the Krishnamurthy formulation for higher-level gains, assuming LIFO organization for the gain buckets.