Average interconnection length and interconnection distribution based on rent's rule

Authors:
C. V. Gura;J. A. Abraham
Affiliations:
Computer Systems Group, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign;Department of ECE, The University of Texas at Austin
Venue:
DAC '89 Proceedings of the 26th ACM/IEEE Design Automation Conference
Year:
1989

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Abstract

In this paper we show that it is necessary to utilize different partitioning coefficients in interconnection length analyses which are based on Rent's rule, depending on whether one- or two-dimensional placement strategies are used. &bgr;, the partitioning coefficient in the power-law relationship &agr;&Bgr;&bgr;, provides a measure of the number of interconnections which cross a boundary enclosing &Bgr; blocks. The partitioning coefficients are &bgr;=p/2 and &bgr;=p for two- and one-dimensional arrays, respectively, where p is the experimental coefficient of the Rent relationship T=&agr;&Bgr;p. Based on these separate partitioning coefficients, an average interconnection length prediction is presented for rectangular arrays that outperforms existing predictions. Examples are given to support this theory.