A statistical methodology for wire-length prediction

In this paper, the classic wire-length estimation problem is addressed and a new statistical wire-length estimation approach that captures the probability distribution function of net lengths after placement and before routing is proposed. These types of models are highly instrumental in formalizing a complete and consistent probabilistic approach to design automation and design closure where, along with optimizing the pertinent cost function, the associated prediction error is also considered. The wire-length prediction model was developed using a combination of parametric and nonparametric statistical techniques. The model predicts not only the length of the net using input parameters extracted from the floorplan of a design, but also probability distributions that a net with given characteristics after placement will have a particular length. The model is validated using the learn-and-test and resubstitution techniques. The model can be used for a variety of purposes, including the generation of a large number of statistically sound, and therefore realistic, instances of designs. The net models were applied to the probabilistic buffer-insertion problem and substantial improvement was obtained in net delay after routing (~ 20%) when compared to a traditional bounding box (BBOX)-based buffer-insertion strategy