A New Wirelength Model for Analytical Placement

Minimization of Half-Perimeter Wire length (HPWL) is a commonly used objective for circuit placement. Analytical placers require approximations of it that are smooth, continuous and differentiable. This paper proposes a new mathematical model to approximate the HPWL cost function. We discuss the theory behind the model and show its convergence properties. We derive the error bounds of the new cost function and show several desirable properties of the new approximation model. We use the global and detailed placements produced by the NTUPlacer on ISPD 2004 benchmark suite to compare the smoothed approximation to two other approximation schemes namely the LogSumExp and CHKS based approximations. Our experiments validate our theoretical results and we show that our scheme has an average of 5% error in the total wire length. We also discuss key implementation issues that can help in keeping the analytical placers based on this approximation numerically stable.