A high-quality mixed-size analytical placer considering preplaced blocks and density constraints

In addition to wirelength, modern placers need to consider various constraints such as preplaced blocks and density. We propose a high-quality analytical placement algorithm considering wirelength, preplaced blocks, and density based on the log-sum-exp wirelength model proposed by Naylor et al. [20] and the multilevel framework. To handle preplaced blocks, we use a two-stage smoothing technique, Gaussian smoothing followed by level smoothing, to facilitate block spreading during global placement. The density is controlled by white-space re-allocation using partitioning and cut-line shifting during global placement and cell sliding during detailed placement. We further use the conjugate gradient method with dynamic step-size control to speed up the global placement and macro shifting to and better macro positions. Experimental results show that our placer obtains the best published results.