Abstract
This paper presents a new method of sizing the widths of the power and ground routes in integrated circuits so that the chip area required by the routes is minimized subject to electromigration and IR voltage drop constraints. The basic idea is to transform the underlying constrained nonlinear programming problem into a sequence of linear programs. Theoretically, we show (that the sequence of linear programs always converges to the optimum solution of the relaxed convex optimization problem. Experimental results demonstrate that the proposed sequence-of-linear-program method Is orders of magnitude faster than the best-known method based on conjugate gradients with constantly better solution qualities.
Highlights
POWER /Ground (P/G) networks connect the power/ground supplies in the circuit modules to the P/G pads on a chip
A computer-aided design (CAD) tool for P/G network optimization has been developed based on the proposed sequence-of-linear-programming method
For P/G network pg20x20, the new method reduces the chip area used by 90.6%, while the conjugate gradient method reduces the chip area used by 85.3%
Summary
POWER /Ground (P/G) networks connect the power/ground supplies in the circuit modules to the P/G pads on a chip. One major obstacle is that these methods are based on constrained nonlinear programming, a process known to be computationally intensive (NP-hard [12]) These methods are applicable only to small size problems, while P/G networks in today’s very large sale integration (VLSI) design may contain millions of wire segments (millions of variables). We present a new method capable of solving the power/ground optimization problem orders of magnitude faster than the best known method. Our method is inspired by a key observation made by Chowdhury that if currents in wire segments are fixed, and voltages are used as variables, the resulting optimization problem is convex [8]. Instead of using the conjugate gradient method as in [8], we show that the problem can be solved elegantly by a sequence of linear programs.
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