Abstract-Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matching-based clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9% for 100 runs and 3.0 to 20.6% for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.
Abstract-Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matching-based clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9% for 100 runs and 3.0 to 20.6% for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.
Abstract-Many previous works in partitioning have used some underlying clustering algorithm to improve performance. As problem sizes reach new levels of complexity, a single application of a clustering algorithm is insufficient to produce excellent solutions. Recent work has illustrated the promise of multilevel approaches. A multilevel partitioning algorithm recursively clusters the instance until its size is smaller than a given threshold, then unclusters the instance while applying a partitioning refinement algorithm. In this paper, we propose a new multilevel partitioning algorithm that exploits some of the latest innovations of classical iterative partitioning approaches. Our method also uses a new technique to control the number of levels in our matching-based clustering algorithm. Experimental results show that our heuristic outperforms numerous existing bipartitioning heuristics with improvements ranging from 6.9 to 27.9% for 100 runs and 3.0 to 20.6% for just ten runs (while also using less CPU time). Further, our algorithm generates solutions better than the best known mincut bipartitionings for seven of the ACM/SIGDA benchmark circuits, including golem3 (which has over 100 000 cells). We also present quadrisection results which compare favorably to the partitionings obtained by the GORDIAN cell placement tool. Our work in multilevel quadrisection has been used as the basis for an effective cell placement package.
Iterative improvement partitioning algorithms such as the FM algorithm of Fiduccia and Mattheyses [8], the algorithm of Krishnamurthy [13], and Sanchis's extensions of these algorithms to multiway partitioning [16] 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 [13], [16]) or as firstin-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 [16] and for more sophisticated partitioning strategies such as the two-phase FM methodology [2]. 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.
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