A novel damped-wave framework for macro placement.

In this paper, we present a damped-wave constructive macro placement framework which packs big macros to optimize both wirelength and routability simultaneously. Unlike traditional V-shaped and Λ-shaped multilevel frameworks which might lack respective local and global information during processing, our damped-wave framework considers both local and global information by the following two major techniques: (1) macro clustering to improve scalability, and (2) constructive macros declustering to assist a standard-cell placer to obtain better solutions. We also present a macro-grouping cost model to remedy the key drawback of ignoring the mismatches of standard-cell locations between the prototyping and the final standard-cell placement stages in existing three-stage mixed-size placers (containing prototyping, macro placement, and standard cell placement). We further propose the regularity penalty model to guide macros to form an integral, regular region during macro placement, facilitating the succeeding placement of standard cell. Compared with manual placement from industrial and a leading mixed-size placer, experimental results show that our damped-wave multilevel framework and cost models are efficient and effective in reducing half-perimeter wirelength and routed wirelength and overflows. In particular, our work provides a new research direction on effective frameworks for large-scale designs, which readily apply to many optimization problems limited with scalability.