An Efficient Practical Heuristic For Good Ratio-Cut Partitioning

• Authors: Sachin B. Patkar;H. Narayanan
• Venue: VLSID '03 Proceedings of the 16th International Conference on VLSI Design
• Year: 2003

We present an efficient heuristic for finding good bipartitionsof the vertex set of a graph in the sense of the well-knownmeasure of ratioCut [2, 8] (essentially the ratio betweenweight of cut edges and the product of weights of thenodesets of the bipartition). The widely accepted ratioCutbipartitioning algorithm of Wei and Cheng [13] is similarin spirit to the Fiduccia-Mattheyeses [9] algorithm (F-Malgorithm). Our approach makes use of F-M algorithm asthe first phase that takes in as an input, random bipartitions.In the later phase of our algorithm we make use of anew coarsening strategy and follow it up with a submodularfunction optimization algorithm on the coarsened graph.We also present the comparison of results of this approachapplied to benchmark circuits with the well-established algorithmssuch as the Wei-Cheng algorithm [13] for ratioCutbipartitioning and pmetis of Metis [7] package. The comparativestudy not only shows that this new approach indeedproduces good quality ratioCut bipartitions, but also thefact that this approach has the potential of finding a largenumber of such good partitions in comparison with otherapproaches. The key subroutine in our heuristic strategiesis based on the recent finding published in [12] about therole of submodular functions in designing new heuristicsand approximate algorithms to some NP-hard problems.