Wire-length Prediction using Statistical and Probabilistic Techniques

We address the classic wire-length estimation problem and propose a new statistical wire-length estimation approach that captures the probability distribution function of net lengths after placement and before routing. 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 non-parametric 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 obtained after placement will have a particular length. The model is validated using both 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. We applied the net models to the probabilistic buffer insertion problem and obtained substantial improvement in net delay after routing (∼40%) when compared to a traditional bounding box-based buffer insertion strategy.