PaRS: Fast and near-optimal grid-based cell sizing for library-based design

We propose PaRS, a parallel and randomized tool which solves the discrete gate sizing (cell sizing) problem on a grid. PaRS is formulated based on an optimization framework known as Nested Partitions which uses parallelism and randomization from a novel perspective to better identify the optimization direction. It achieves near-optimal solutions for minimizing total power and area subject to meeting a delay constraint. The embarrassingly-parallel nature of PaRS makes it highly efficient. We show small algorithm run-times, in at most minutes for circuits with over 47,000 cells. We make comparison with the optimal solution generated by a custom and parallel branch-and-bound algorithm. Consequently, we are able to generate the optimal solution within hours. While the optimal algorithm uses up to 200 nodes in our grid, PaRS achieves its speedups and near-optimal solutions using only 20 nodes.