Timing-Driven Placement Based on Dynamic Net-Weighting for Efficient Slack Histogram Compression

Timing-driven placement (TDP) finds new legal locations for standard cells so as to minimize timing violations while preserving placement quality. Although violations may arise from unmet setup or hold constraints, most TDP approaches ignore the latter. Besides, most techniques focus on reducing the worst negative slack and let the improvements on total negative slack as a secondary goal. However, to successfully achieve timing closure, techniques must also reduce the total negative slack, which is known as slack histogram compression. This paper proposes a new Lagrangian Relaxation formulation for TDP to compress both late and early slack histograms. To solve the problem, we employ a discrete local search technique that uses the Lagrange multipliers as net-weights, which are dynamically updated using an accurate timing analyzer. To preserve placement quality, our technique uses a small fixed-size window that is anchored in the initial location of a cell. For the experimental evaluation of the proposed technique, we relied on the ICCAD 2014 TDP contest infrastructure. The results show that our technique significantly reduces the timing violations from an initial global placement. On average, late and early total negative slacks are improved by 85.03% and 42.72%, respectively, while the worst slacks are reduced by 71.55% and 34.40%. The overhead in wirelength is less than 0.1%.