language: en

Optimal Wire-Sizing Formula Under the Elmore Delay Model

Chung-Ping Chen, Yao-Ping Chen, and D. F. Wong
Department of Computer Sciences, University of Texas,
Austin, Texas 78712

Abstract In this paper, we consider non-uniform wire-sizing. Given a wire segment of length L, let f(x) be the width of the wire at position x, 0 x L. We show that the optimal wire-sizing function that minimizes the Elmore delay through the wire is f(x) = ae bx , where a &gt; 0 and b &gt; 0 are constants that can be computed in O(1) time. In the case where lower bound (L &gt; 0) and upper bound (U &gt; 0) on the wire widths are given, we show that the optimal wire-sizing function f(x) is a truncated version of ae bx that can also be determined in O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree.

1 Introduction