This paper proposes a placement method for a mixed set of hard, soft, and pre-placed modules, based on a placement topology representation called sequence-pair. Under one sequence-pair, a convex optimization problem is e ciently formulated and solved to optimize the aspect ratios of the soft modules. The method is used in two ways: i directly applied in simulated annealing to present the most exact placement method, ii applied as a post process in an approximate placement method for faster computation. The performance of these two methods are reported using MCNC benchmark examples.
Hiroshi Murata, Ernest S. Kuh