New spectral linear placement and clustering approach

Abstract

This paper addresses the linear placement problem by using a spectral approach. It has been demonstrated that, by giving a more accurate representation of the linear placement problem, a linear objective function yields better placement quality in terms of wire length than a quadratic objective function as in the eigenvector approach [4][11][6]. On the other hand, the quadratic objective function has an advantage in that it tends to place components more sparsely than the linear objective function, resulting in a continuous solution closer to a physically feasible discrete solution. In this paper, we propose an /spl alpha/-order objective function to capture the strengths of both the linear and quadratic objective functions. We demonstrate that our approach yields improved spectral placements. We also present a bottom-up clustering algorithm which iteratively collapses pairs of nodes in a graph using local and global connectivity information, where the global connectivity information is derived from the clustering property of the eigenvector approach. The effect of our new spectral linear placement and clustering approach is demonstrated on benchmark circuits from MCNC.