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IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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In this article, we first show that existing net ordering formulations to minimize noise are no longer sufficient with the presence of inductive noise, and shield insertion is needed to minimize inductive noise. Using a Keff model as the figure of merit for inductive coupling, we then formulate two simultaneous shield insertion and net ordering (SINO) problems: the optimal SINO/NF problem to find a minimal area SINO solution that is free of capacitive and inductive noise, and the optimal SINO/NB problem to find a minimal area SINO solution that is free of capacitive noise and is under the given inductive noise bound. We reveal that both optimal SINO problems are NP-hard, and propose effective approximate algorithms for the two problems. Experiments show that our SINO/NB algorithm uses from 51% to 82% fewer shields compared to uniform shield insertion and net ordering (US + NO), and uses from 4% to 47% fewer shields compared to separated net ordering and shield insertion (NO + SI). Furthermore, the SINO/NB solutions under practical noise bounds use from 38% to 61% fewer shields compared to SINO/NF solutions, and use up to 36% fewer shields compared to the theoretical lower bound for optimal SINO/NF solutions. Moreover, we show that the Keff model has a high fidelity versus the noise voltage computed using accurate RLC circuit models and SPICE simulations. To the best of our knowledge, it is the first work that presents an in-depth study on the automatic layout optimization of multiple nets to minimize both capacitive and inductive noise.