Jianli Chen
ABSTRACT
Modern circuits often contain standard cells of different row heights to meet various design requirements. Higher cells give larger drive strengths at the costs of larger areas and power. Multi-row-height standard cells incur challenging issues to layout designs, especially the mixed-cell-height legalization problem due to the heterogeneous cell structures. Honoring the good cell positions from global placement, we present in this paper a fast and near-optimal algorithm to solve the legalization problem. Fixing the cell ordering from global placement and relaxing the right boundary constraints, we first convert the problem into a linear complementarity problem (LCP). With the converted LCP, we split its matrices to meet the convergence requirement of a modulus-based matrix splitting iteration method (MMSIM), and then apply the MMSIM to solve the LCP. This MMSIM method guarantees the optimality if no cells are placed beyond the right boundary of a chip. Finally, a Tetris-like allocation approach is used to align cells to placement sites on rows and fix the placement of out-of-right-boundary cells, if any. Experimental results show that our proposed algorithm can achieve the best cell displacement and wirelength among all published methods in reasonable runtimes. The MMSIM optimality is theoretically proven and empirically validated. In particular, our formulation provides new generic solutions and research directions for various optimization problems that require solving large-scale quadratic programs efficiently.
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Index Terms
- Toward Optimal Legalization for Mixed-Cell-Height Circuit Designs
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