An improved multi-level framework for force-directed placement

One of the greatest impediments to achieving high quality placements using force-directed methods lies in the large amount of overlap initially present in these techniques. This overlap makes the determination of cell ordering difficult and can lead to the inadvertent separation of highly connected cells by the spreading forces. We show that a multi-level clustering strategy can minimize the ill effects of overlap and improve the quality of placements generated by the force-directed tool FDP. Moreover, we present a means of improving initial cell ordering through the unification of min-cut partitioning and force-based placement, and describe an enhanced median improvement heuristic which further aids in minimizing HPWL. Numerical results are presented showing that our flow generates placements which are, on average, 15% better than mPG and 4% better than Capo 9.0 on mixed-size designs.