Optimal wire-sizing formula under the Elmore delay model

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, O⩽x⩽L. We show that the optimal wire-sizing function that minimizes the El more delay through the wire as f(x)=ae^-bx , where a>0 and b>0 are constants that can be computed an O(1) time. In the case where lower bound (L>0) and upper bound (U>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 an O(1) time. Our wire-sizing formula can be iteratively applied to optimally size the wire segments in a routing tree