Force-Directed Methods for Generic Placement

This paper describes the implementation of a wire length-driven force-directed placer named FDP for generic placement. Specifically, it describes efficient force computation for cell spreading, numerical instabilities during force-directed placement, a means to avoid instabilities, and metrics for proper assessment of cell distribution throughout the placement region. It demonstrates that one of the greatest impediments to achieving high-quality placements using a force-directed placer lies in the large amount of cell overlap present in initial placements. This overlap makes the determination of cell ordering difficult and can lead to the inadvertent separation of highly connected cells. It is shown that median improvement and multilevel clustering improve cell ordering and aid in wire length minimization. Numerical results are presented for both standard cell and mixed-size placement problems. For standard cell problems, the tool generates placements that are, on average, 3% better than Capo9.0, but 5% worse than FengShui2.6. For mixed-size problems, FDP generated placements that are, on average, 2%-5% better than Capo9.0 and -5%--2% better than Fengshui2.6, depending on the presence (or absence) of pin offsets. Run times for FDP are higher than both Capo9.0 and FengShu2.6, although reasonable