Netlist-Aware Mixed-Cell-Height Legalization

Mixed cell heights pose significant challenges to placement in large-scale integrated circuits. In particular, the heterogeneity of cells remarkably complicates the legalization of mixed-cell-height cells. To preserve the global placement results as much as possible, we propose to directly optimize the total displacement through l1-norm minimization. For illegal cells that extend beyond the chip boundaries, the netlist information of cells is taken into account and a mixed-integer programming model is employed to determine the optimal placement that minimizes the half-perimeter wirelength (HPWL) variation. This joint optimization strikes a balance between minimizing geometric displacement and HPWL, ensuring that the legalization process remains compact to achieve better placement performance. Experimental evaluations on mixed-cell-height benchmarks demonstrate that the proposed approach achieves smaller total displacement and notably lower HPWL variation within practical time limits compared with state-of-the-art legalization methods. Moreover, this work provides a scalable foundation for future extensions to three-dimensional (3D) IC placement legalization.