A fast hierarchical quadratic placement algorithm

Placement is a critical component of today's physical-synthesis flow with tremendous impact on the final performance of very large scale integration (VLSI) designs. Unfortunately, it accounts for a significant portion of the overall physical-synthesis runtime. With the complexity and the netlist size of today's VLSI design growing rapidly, clustering for placement can provide an attractive solution to manage affordable placement runtimes. However, such clustering has to be carefully devised to avoid any adverse impact on the final placement solution quality. This paper presents how to apply clustering and unclustering strategies to an analytic top-down placer to achieve large speedups without sacrificing (and sometimes even enhancing) the solution quality. The authors' new bottom-up clustering technique, called the best choice (BC), operates directly on a circuit hypergraph and repeatedly clusters the globally best pair of objects. Clustering score manipulation using a priority-queue (PQ) data structure enables identification of the best pair of objects whenever clustering is performed. To improve the runtime of PQ-based BC clustering, the authors proposed a lazy-update technique for faster updates of the clustering score with almost no loss of the solution quality. A number of effective methods for clustering score calculation, balancing cluster sizes, handling of fixed blocks, and area-based unclustering strategy are discussed. The effectiveness of the resulting hierarchical analytic placement algorithm is tested on several large-scale industrial benchmarks with mixed-size fixed blocks. Experimental results are promising. Compared to the flat analytic placement runs, the hierarchical mode is 2.1 times faster, on the average, with a 1.4% wire-length improvement.