A Fast, Robust Network Flow-based Standard-Cell Legalization Method for Minimizing Maximum Movement

The standard-cell placement legalization problem has become critical due to increasing design rule complexity and design utilization at 16nm and lower technology nodes. An ideal legalization approach should preserve the quality of the input placement in terms of routability and timing, as well as effectively manage white space availability and have low runtime. In this work, we present a robust legalization algorithm for standard cell placement that minimizes maximum cell movements fast and effectively based on a novel network-flow approach. The idea is inspired by path augmentation but with important differences. In contrast to the classical path augmentation approaches, we resolve bin overflows by finding several candidate paths that guarantee realizable (legal) flow solutions. In addition, we show how the proposed algorithm can be seamlessly extended to handle relevant cell edge spacing design rules. Our experimental results on the ISPD 2014 benchmarks illustrate that our proposed method yields 2.5x and 3.3x less maximum and average cell movement, respectively, and the runtime is significantly (18x) lower compared to best-in-class academic legalizers.