Speeding up Incremental Legalization with Fast Queries to Multidimensional Trees

Abstract

Circuit legalization removes overlaps and keeps cell alignment with power rails while minimizing total cell displacement. Legalization is applied not only after global placement, but also after incremental optimization steps like detailed placement, gate sizing, and buffer insertion. Applying full legalization after such incremental optimizations is too time-consuming. That is why physical synthesis has been shifting from entire circuit legalization to incremental mode legalization, which keeps legality after every primitive transformation. Unfortunately, recent incremental legalization strategies employ data structures that are not suitable for handling geometric data. This work proposes a new technique that relies on an R-tree, a data structure tailored to efficient geometric data storage where objects are represented by their minimum bounding box rectangles, which allows for fast spatial queries. As compared with state-of-the-art incremental legalization algorithms, the proposed technique is at least 6 times faster and performs as many successful legalizations.