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Advancing Steiner Trees: Implementing Buffered Structures in Difficult Instances

This paper delves into the evolution of Buffered Steiner Trees, exploring the challenges faced in difficult instances and presenting innovative solutions. From the late 1980s to the present, it discusses the adoption of Timing-driven Steiner Trees and Blockage Aware Trees. The text addresses the significance of Buffer-Aware Trees and the complexities of constructing these tree structures efficiently. Various techniques like Dynamic Programming Buffer Insertion are highlighted, along with the Texas Two-Step Optimal C-Tree Algorithm, offering insights into constructing clustered trees based on polarity and Manhattan distance. The discussion touches upon the intricacies of difficult Steiner instances, emphasizing the trade-offs involving polarity, size, timing, buffers, and wire length.

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Advancing Steiner Trees: Implementing Buffered Structures in Difficult Instances

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  1. Buffered Steiner Trees for Difficult Instances Charles J. Alpert, Gopal Gandham, Milos Hrkic, John Lillis, Jiang Hu, Andrew B. Kahng, Bao Liu, Stephen T. Quay, Sachin S. Sapatnekar, Andrew J. Sullivan

  2. Late 1980s Min-Cost Steiner Tree

  3. Timing-driven Steiner Tree Early 1990s

  4. Buffered Steiner Tree Mid 1990s

  5. Present Blockage Aware Trees

  6. Ripping out Synthesis Trees • Ugly pre-PD buffered trees • Inverted sinks • Trivial van Ginneken/Lillis change • Normal sinks: one positive candidate • Inverted sinks: one negative candidate • No big deal

  7. + + + + _ _ _ _ _ _ _ Or Is It?

  8. + + + + _ _ _ _ _ _ _ But Look What Happens

  9. Buffer Aware Trees

  10. Unrouted net with placed pins Construct Steiner Tree Simultaneous Tree Construction And Buffer Insertion Dynamic Programming Buffer Insertion Buffered Steiner Tree The Texas Two Step Optimal

  11. C-Tree Algorithm • A-, B-, H-, O-, P-, trees taken • Cluster sinks by • Polarity • Manhattan distance • Criticality • Two-level tree • Form tree for each cluster • Form top-level tree

  12. C-Tree Example

  13. Net n8702 (44 sinks)

  14. Net n8702

  15. Flat C-Tree

  16. C-Tree 4 clusters

  17. C-Tree 2 clusters

  18. Difficult Steiner Instances • Polarity/size makes it hard • 3d trade-off • Timing • Buffers • Wire length • Work on it!

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