Optimal wire-sizing formula under the Elmore delay model

In this paper, we consider non-uniform wire-sizing. Given a wire segment of length /spl Lscr/, let f(x) be the width of the wire at position x, O/spl les/x/spl les//spl Lscr/. We show that the optimal wire-sizing function that minimizes the El more delay through the wire as f(x)=ae/sup -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/sup -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.