Recursive Function Smoothing of Half-Perimeter Wirelength for Analytical Placement

Inspired by recent success of analytical placers that use a logarithm-sum-exponential (LSE) to smooth half-perimeter wirelength (HPWL), the authors consider in this paper two alternative smoothing methods for HPWL by recursive extension of two-variable max functions. A limited memory quasi-Newton solver is applied to solve the objective function combining both the smoothing function of HPWL and the penalty function that arises from cell density constraints. Experimental results show that our flow using these two smoothing functions and the solver produces placements with comparable HPWL compared to LSE smoothing-based methods. The placement flow also produces placements with comparable routability and routed wirelength but with shorter runtime