Noise-constrained performance optimization by simultaneous gate and wire sizing based on Lagrangian relaxation

Noise, as well as area, delay, and power, is one of the most important concerns in the design of deep sub-micron ICs. Currently existing algorithms can not handle simultaneous switching conditions of signals for noise minimization. In this paper, we model not only physical coupling capacitance, but also simultaneous switching behavior for noise optimization. Based on Lagrangian relaxation, we present an algorithm that can optimally solve the simultaneous noise, area, delay, and power optimization problem by sizing circuit components. Our algorithm, with linear memory requirement overall and linear runtime per iteration, is very effective and efficient. For example, for a circuit of 6144 wires and 3512 gates, our algorithm solves the simultaneous optimization problem using only 2.1 MB memory and 47 minute runtime to achieve the precision of within 1% error on a SUN UltraSPARC-I workstation.