A Priori Wirelength Estimation: Statistical Models, Bounds and Applications

A priori wirelength prediction is an important and often addressed problem in physical design with numerous and high impact applications. In the last four decades a wide spectrum of insightful and sophisticated techniques for a priori wirelength prediction have been developed. In addition, highly accurate predictions and models have been reported for average wirelength and wirelength distributions. At the same time, although it was realized that the accuracy of prediction for the wirelength of a specific net is bounded, several papers reported good predictors for individual nets. Our goal is to address the a priori wirelength prediction problem from a new viewpoint. We use a system of rigorous statistical modeling and validation techniques to establish quantitative bounds on the accuracy of a priori wirelength prediction. For each design, we produced a large number of competitive implementations by varying the placement parameters. The data is used for the development of datadriven statistical models for an individual netlist, total wirelength, and distribution of wirelengths in terms of their quantitative predictability. The models are validated and their accuracy quantified using resubstitution. At the same time, we show that both total wirelength and the distribution of wirelength can be very accurately predicted. Using the derived statistical models, we also introduce two new applications for a priori total wirelength predictions: rapid exploration of the placement solution space and identification of placement invariant long nets. Finally, an apparent discrepancy between the previous and new results is analyzed.