Multiway partitioning with pairwise movement

It is well known that the recursive bipartitioning approach outperforms the direct non-recursive approach in solving the multiway partitioning problem. However, little progress has been made to identify and overcome the weakness of the direct (alternatively called flat) approach. We make the first observation that the performance of iterative improvement based flat multiway partitioner K-FM (L.A. Sanchis, 1989; 1993) is not suitable for today's large scale circuits. Then, we propose a simple yet effective hill climbing method called PM (Pairwise cell Movement) that overcomes the limitation of K-FM and provides partitioners the capability to explore wider range of solution space effectively while ensuring convergence to satisfying suboptimal solutions. The main idea is to reduce the multiway partitioning problem to sets of concurrent bipartitioning problems. Starting with an initial multiway partition of the netlist, we apply 2-way FM (C. Fiduccia and R. Mattheyses, 1982) to pairs of blocks so as to improve the quality of overall multiway partitioning solution. The pairing of blocks is based on the gain of the last pass, and the Pairwise cell Movement (PM) passes continue until no further gain can be obtained. We observe that PM passes are effective in distributing clusters evenly into multiple blocks to minimize the connections across the multiway cutlines. Our iterative improvement based flat multiway partitioner K-PM/LR improves K-FM by a surprising average margin of up to 86.2% and outperforms its counterpart recursive FIM by up to 17.3% when tested on MCNC and large scale ISPD98 benchmark circuits (C.J. Alpert, 1998).