Legalization algorithm for multiple-row height standard cell design

Typical standard cell placement algorithms assume that all cells are of the same height such that cells can be aligned along the placement rows. However, modern standard cell designs are getting more complicated and multiple-row height cell becomes more common. With multiple-row height cells, placement of cells are not independent among different rows. It turns out that most of the commonly used detailed placement and legalization techniques cannot be extended easily to handle the problem. We propose a novel algorithm in handling legalization of placement involving multiple-row height cells. The algorithm can efficiently legalize a local region of cells with various heights, which is especially useful for local cell movement, cell sizing, and buffer insertion. Experiments on the application of the technique in detailed placement show that our approach can effectively and efficiently legalize global placement results and obtain significant improvement in the objective function.