A placement problem can be formulated as a quadratic program with non-linear constraints. Those constraints make the problem hard. Omitting the constraints and solving the unconstraint problem results in placement with substantial cell overlaps. To remove the overlaps, we introduce fixed points into the non-constrained quadratic-programming formulation. Acting as pseudo cells at fixed locations, they can be used to pull cells away from the dense regions to reduce overlapping. In this paper, we present a large-scale placement algorithm based on fixed-point addition.
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