Rapid gate sizing with fewer iterations of Lagrangian Relaxation

Existing Lagrangian Relaxation (LR) based gate sizers take many iterations to converge to a competitive solution. In this paper, we propose a novel LR based gate sizer which dramatically reduces the number of iterations while achieving a similar reduction in leakage power and meeting the timing constraints. The decrease in the iteration count is enabled by an elegant Lagrange multiplier update strategy for rapid coarse-grained optimization as well as finer-grained timing and power recovery techniques, which allow the coarse-grained optimization to terminate early without compromising the solution quality. Since LR iterations dominate the total runtime, our gate sizer achieves an average speedup of 2.5x in runtime and saves 1% more power compared to the previous fastest work.