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Cpi > 0 only if bpi > 0 or apq,i, > 0 for any q and j; Following the notations in [8], we call the class of functions as CH-posynomials. Gate2 Definition 1 Eqn. (1) is a simple CH-posynomial if all coefficients are constants independent of X. Definition 2 Eqn. (1) is a general CH-posynomial if coefjicients are functions of xi and x, satisfying the following conditions: ap,,ij monotonically increases with respect to zx while monotonically decreases with respect to x,, and br,, monotonically increases with respect to xi while cp,, monotonically decreases with respect to xi.

E. L < f (x) < U, 0 < x < L, we show that the optimal wire-sizing function f (x) is a truncated version of ae-b. which can also be determined in O(1) time. Our wiresizing formula can be iteratively applied to optimally size the wire segments in a routing tree. The remainder of this paper is organized as follows. In wire load - Figure 1: Non-uniform wire-sizing. Section 2, we show how to compute the Elmore delay for non-uniformly sized wire segments. 1, we derive the optimal wire-sizing function when the wire widths are not constrained to be within any bounds.

Identical width at every position on the wire. In order to achieve non-uniform wire-sizing, existing algorithms have to chop wire segments into large number of small segments. Consequently, the number of variables in the optimization problem is increased substantially and thus results in long runtime and large storage. In this paper, we consider non-uniform wire-sizing. Given a wire segment W of length L, a source with driver resistance Rd, and a sink with load capacitance CL. For each x e [0, L], let f (x) be the wire width of W at position x.

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ACM-SIGDA Physical Design Workshop #5 1996: Proceedings by ACM-SIGDA


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