Optimal partitioners and end-case placers for standard-cell layout

We study alternatives to classic Fiduccia-Mattheyses (FM)-based partitioning algorithms in the context of end-case processing for top-down standard-cell placement. While the divide step in the top-down divide and conquer is usually performed heuristically, we observe that optimal solutions can be found for many sufficiently small partitioning instances. Our main motivation is that small partitioning instances frequently contain multiple cells that are larger than the prescribed partitioning tolerance, and that cannot be moved iteratively while preserving the legality of a solution. To sample the suboptimality of FM-based partitioning algorithms, we focus on optimal partitioning and placement algorithms based on either enumeration or branch-and-bound that are invoked for instances below prescribed size thresholds, e.g.,