A Robust Newton Iteration Method for Mixed-Cell-Height Circuit Legalization Under Technology and Region Constraints

Abstract

The evolution of advanced technology nodes has prompted a shift toward mixed-cell-height circuit design, while the introduction of technology and fence region constraints further increases the complexity of placement. In this paper, we innovatively transform the mixed-cell-height circuit legalization problem into a generalized absolute value equation (GAVE) and propose a novel and effective robust Newton (RN) iteration method to address the challenge of the legalization problem. First, the window-based cell insertion technique is applied to obtain the initial cell row allocation and cell order, and the cells are allocated to the matching region based on the R-tree structure. Then, the legalization problem of cells within the region is transformed into a GAVE, and a robust Newton iteration method is proposed to solve the GAVE. Finally, the maximum displacement cells and technology violation cells are optimized based on a greedy method. Experimental results confirm the efficiency and robustness of the proposed method compared with the state-of-the-art methods.