Faster and Better Spectral Algorithms for Multi-Way Partitioning

In this paper, two faster and better spectral algorithms are presented for the multi-way circuit partitioning problem with the objective of minimizing the Scaled Cost. As pointed out in [3], the problem can be approximately transformed into the vector partitioning problem by mapping each circuit component to a multi-dimensional vector. The common key idea of our two algorithms for solving the vector partitioning problem is to first treat the set of vectors as a cluster, and then repeatedly select a cluster, which gives the maximum cost improvement among all the current clusters, and partition it into two new clusters. The bipartitioning process is continued until the number of clusters is equal to the required number of partitions. The experimental results indicate that the two algorithms significantly outperform MELO+DPRP [3] in both the run time and partitioning result.