The interpretation and application of Rent´s rule

This paper provides a review of both Rent\´s rule and the placement models derived from it. It is proposed that the power-law form of Rent\´s rule, which predicts the number of terminals required by a group of gates for communication with the rest of the circuit, is a consequence of a statistically homogeneous circuit topology and gate placement. The term "homogeneous" is used to imply that quantities such as the average wire length per gate and the average number of terminals per gate are independent of the position within the circuit. Rent\´s rule is used to derive a variety of net length distribution models and the approach adopted in this paper is to factor the distribution function into the product of an occupancy probability distribution and a function which represents the number of valid net placement sites. This approach places diverse placement models under a common framework and allows the errors introduced by the modeling process to be isolated and evaluated. Models for both planar and hierarchical gate placement are presented.