NGLIC: A Nonaligned-Row Legalization Approach for 3-D Interdie Connection

3-D placement is an important stage in 3-D physical synthesis. In addition to the need to place the standard cells or Macros inside the die, the placement of interdie connections also needs to be considered. As the density of the interdie connections gradually increases, their placement becomes more critical. However, unlike standard cells, the interdie connection does not need to be aligned into rows, which leads to a larger legalization solution space. Legalization aims at minimizing the total and maximum displacement to maintain the quality of global placement on the premise of no violation of the physical circuit constraint. In this article, we propose a two-stage legalization approach (NGLIC) for nonaligned-row interdie connections. In the initial stage, a single-row height legalization algorithm is used for dense placement. Afterward, the unequal multirow height legalization (UML) is designed for sparse placement in the post-optimization stage. A pruning scheme is adopted to identify and eliminate redundant computations. The performance, effectiveness, and configuration are analyzed empirically based on ICCAD 2022 benchmarks. Compared to the state-of-the-art multirow or single-row height legalization, our approach outperforms well-known algorithms, such as multirow global legalization (MGL) and Abacus by at least 24% averaged total displacement, 3% averaged maximum displacement, and 31% averaged HPWL Growth. Our case study also illustrates the effectiveness of UML and NGLIC. In addition, the effectiveness of pruning is also validated by experiments that show savings of 33% redundant computations.