On rent's rule for rectangular regions

摘要

A priori wirelength estimates are based on a terminal-gate relationship known as Rent's rule. Conventional models apply Rent's rule in 2D on square or diamond-shaped regions. However, more advanced applications of wirelength estimation require the use of Rent's rule on layout regions with different shapes. In this paper, we systematically study the layout Rent parameters of rectangular regions in a 2D layout medium. For this purpose, we derive a theoretical model for the pin versus gate relationship for layout regions of any given shape. Using this model to find an estimation of the layout Rent parameters of rectangular regions with a given aspect ratio, we show that there is a significant dependency of the Rent coefficient on that aspect ratio. We experimentally verify these results with synthetic, as well as industrial benchmark circuits.

Furthermore, our model relates the layout Rent parameters of a circuit to its intrinsic partitioning properties. This leads to a fundamental limit onthe value of the layout Rent exponent for circuits, embedded in a 2D layout medium.