Linear-time Mixed-Cell-Height Legalization for Minimizing Maximum Displacement

ABSTRACTDue to the aggressive scaling of advanced technology nodes, multiple-row-height cells have become more and more common in VLSI design. Consequently, the placement of cells is no longer independent among different rows, which makes the traditional row-based legalization techniques obsolete. In this work, we present a highly efficient linear-time mixed-cell-height legalization approach that optimizes both the total cell displacement and the maximum cell displacement. First, a fast window-based cell insertion technique introduced in [4] is applied to obtain a feasible initial row assignment and cell ordering which is known to be good for total displacement consideration. In the second stage, we use an iterative cell swapping algorithm to change the row assignment and the cell order of the critical cells for maximum displacement reduction. Then we develop an optimal linear time DAG-based fixed row and fixed order legalization algorithm to minimize the maximum cell displacement. Finally, we propose a cell shifting heuristic to reduce the total cell displacement without increasing the maximum cell displacement. Using the proposed approach, the quality provided by the global placement can be preserved as much as possible. Compared with the state-of-the-art work [4], experimental results show that our proposed algorithm can reduce the maximum cell displacement by more than 11% on average with similar average cell displacement.