On implementation choices for iterative improvement partitioning algorithms

Iterative improvement partitioning algorithms such as the FM algorithm of Fiduccia and Mattheyses (1982), the algorithm of Krishnamurthy (1984), and Sanchis's extensions of these algorithms to multiway partitioning (1989) all rely on efficient data structures to select the modules to be moved from one partition to the other. The implementation choices for one of these data structures, the gain bucket, is investigated. Surprisingly, selection from gain buckets maintained as last-in-first-out (LIFO) stacks leads to significantly better results than gain buckets maintained randomly (as in previous studies of the FM algorithm or as first-in-first-out (FIFO) queues. In particular, LIFO buckets result in a 36% improvement over random buckets and a 43% improvement over FIFO buckets for minimum-cut bisection. Eliminating randomization from the bucket selection not only improves the solution quality, but has a greater impact on FM performance than adding the Krishnamurthy gain vector. The LIFO selection scheme also results in improvement over random schemes for multiway partitioning and for more sophisticated partitioning strategies such as the two-phase FM methodology. Finally, by combining insights from the LIFO gain buckets with the Krishnamurthy higher-level gain formulation, a new higher-level gain formulation is proposed. This alternative formulation results in a further 22% reduction in the average cut cost when compared directly to the Krishnamurthy formulation for higher-level gains, assuming LIFO organization for the gain buckets.