An Accelerated Newton-Based Matrix Splitting Iteration Method for Mixed-Cell-Height Circuit Legalization

The advancement of technology nodes has intensified the focus on mixed-cell-height circuit design, posing challenges to traditional legalization techniques. In this paper, we propose a novel and efficient accelerated Newton-based matrix splitting (ANMS) iteration method to address the mixed-cell-height circuit legalization problem. Our approach reformulates this problem into a generalized absolute value equation and leverages matrix splitting and the latest estimate vector to enhance computational efficiency. We also introduce a relaxation variant within the ANMS framework, namely, the accelerated Newton-based successive overrelaxation (ANSOR) method, which is particularly effective in scenarios requiring high computational performance and precise parameter tuning. The proposed method achieves linear computational complexity. Furthermore, we perform an in-depth analysis of the sufficient convergence conditions for the ANMS method and optimize cells that have excessive displacement. Experimental results show that the proposed ANMS method achieves a speedup of 1.09× – 4.94× compared to state-of-the-art methods, while maintaining the quality of solution. This makes it highly suitable for addressing complex placement design challenges.