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High-correlation 3D routability estimation for congestion-guided global routing

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Abstract

Routability estimation identifies potentially congested areas in advance to achieve high-quality routing solutions. To improve the routing quality, this paper presents a deep learning-based congestion estimation algorithm, which serves to guide the initial pattern routing of a global router to reduce unexpected overflows. Unlike existing methods based on traditional compressed 2D features for model training and prediction, our algorithm extracts appropriate 3D features from the placed netlists. Furthermore, an improved RUDY (Rectangular Uniform wire DensitY) method is developed to estimate 3D routing demands. For the model selection, we employ the U-net model with good image prediction ability as a routability estimator, and the prediction results are used for guiding the initial routing process. Since our training set is formed by cropping training designs, the structural information between two adjacent cropped designs may be missed. Hence, we divide experiments into two parts, experiments based on normal designs and experiments based on big designs. Compared with the state-of-the-art method, experimental results show that our routability estimator can significantly improve the Pearson Correlation Coefficient (PCC) index and reduce the Mean Absolute Normalized Error (MANE) and the Standard Deviation in the Normalized Error (SDNE). Furthermore, our congestion-guided global routing can reduce the routing overflows, wirelength, and via count both on normal designs and big designs, compared to CUGR.

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References

  1. Westra J, Bartels, C, Groeneveld P (2004) Probabilistic congestion prediction. In: Alpert CJ, Groeneveld P (eds) Proceedings of the international symposium on physical design, pp 204–209

  2. Yang X, Kastner R, Sarrafzadeh M (2002) Congestion estimation during top-down placement. IEEE Trans Comput Aided Des Integr Circuits Syst 21(1):72–80

    Article  Google Scholar 

  3. Hsu M-K, Chou S, Lin T-H, Chang Y-W (2011) Routability-driven analytical placement for mixed-size circuit designs. In: Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 80–84. IEEE

  4. Liu W-H, Li Y-L, Koh C-K (2012) A fast maze-free routing congestion estimator with hybrid unilateral monotonic routing. In: Proceedings of the IEEE/ACM International Conference on Computer-Aided Design, pp. 713–719. IEEE

  5. Saeedi M, Zamani MS, Jahanian A (2006) Prediction and reduction of routing congestion. In: Proceedings of the international symposium on physical design, pp 72–77

  6. Saeedi M, Zamani MS, Jahanian A (2007) Evaluation, prediction and reduction of routing congestion. Microelectron J 38(8–9):942–958

    Article  Google Scholar 

  7. Kim M, Hu J, Lee D, Markov IL (2011) A SimPLR method for routability-driven placement. In: Phillips JR, Hu AJ, Graeb H (eds) Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 67–73

  8. He X, Huang T, Xiao L, Tian H, Cui G, Young EFY (2011) Ripple: an effective routability-driven placer by iterative cell movement. In: Phillips JR, Hu AJ, Graeb H (eds) Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 74–79

  9. Xu Y, Zhang Y, Chu C (2009) Fastroute 4.0: Global router with efficient via minimization. In: Proceedings of Asia and South Pacific Design Automation Conference, pp 576–581. IEEE

  10. Spindler P, Johannes FM (2007) Fast and accurate routing demand estimation for efficient routability-driven placement. In: Proceedings of Design, Automation and Test in Europe Conference and Exhibition, pp 1–6 . IEEE

  11. Xie Z, Huang Y-H, Fang G-Q, Ren H, Fang S-Y, Chen Y, Hu J (2018) Routenet: Routability prediction for mixed-size designs using convolutional neural network. In: Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 1–8. IEEE

  12. Liang R, Xiang H, Pandey D, Reddy L, Ramji S, Nam G-J, Hu J (2020) DRC hotspot prediction at sub-10nm process nodes using customized convolutional network. In: Proceedings of the international symposium on physical design, pp 135–142

  13. Hung W-T, Huang J-Y, Chou Y-C, Tsai C-H, Chao M (2020) Transforming global routing report into DRC violation map with convolutional neural network. In: Proceedings of the international symposium on physical design, pp 57–64

  14. Tabrizi AF, Rakai L, Darav NK, Bustany I, Behjat L, Xu S, Kennings A (2018) A machine learning framework to identify detailed routing short violations from a placed netlist. In: Proceedings of ACM/ESDA/IEEE Design Automation Conference, pp 1–6. IEEE

  15. Kirby R, Godil S, Roy R, Catanzaro B (2019) Congestionnet: Routing congestion prediction using deep graph neural networks. In: Proceedings of the IFIP/IEEE International Conference on Very Large Scale Integration, pp 217–222. IEEE

  16. Qi Z, Cai Y, Zhou Q (2014) Accurate prediction of detailed routing congestion using supervised data learning. In: Proceedings of the IEEE International Conference on Computer Design, pp 97–103 . IEEE

  17. Zhou Z, Zhu Z, Chen J, Ma Y, Yu B, Ho T-Y, Lemieux G, Ivanov A (2019) Congestion-aware global routing using deep convolutional generative adversarial networks. In: Proceedings of the ACM/IEEE 1st workshop on machine learning for CAD, pp 1–6. IEEE

  18. Zhou Z, Pan Y, Lemieux GGF, Ivanov A (2023) Medusa: a multi-resolution machine learning congestion estimation method for 2d and 3d global routing. ACM Trans Des Autom Electron Syst. https://doi.org/10.1145/3590768

    Article  Google Scholar 

  19. Chen G, Pui C-W, Li H, Chen J, Jiang B, Young EF (2019) Detailed routing by sparse grid graph and minimum-area-captured path search. In: Proceedings of the Asia and South Pacific Design Automation Conference, pp 754–760

  20. Liu J, Pui C-W, Wang F, Young EF (2020) Cugr: Detailed-routability-driven 3d global routing with probabilistic resource model. In: Proceedings of ACM/IEEE Design Automation Conference, pp 1–6. IEEE

  21. Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: Proceedings of the International Conference on Medical Image Computing and Computer-assisted Intervention, pp 234–241. Springer

  22. Su M, Ding H, Weng S, Zou C, Zhou Z, Chen Y, Chen J, Chang Y (2022) High-correlation 3d routability estimation for congestion-guided global routing. In: Proceedings of Asia and South Pacific Design Automation Conference, pp 580–585

  23. Szegedy C, Liu W, Jia Y, Sermanet P, Reed SE, Anguelov D, Erhan D, Vanhoucke V, Rabinovich A (2015) Going deeper with convolutions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp 1–9

  24. Alhyari A, Shamli A, Abuwaimer Z, Areibi S, Grewal G (2019) A deep learning framework to predict routability for fpga circuit placement. In: Proceedings of the International Conference on Field Programmable Logic and Applications, pp 334–341. IEEE

  25. Alawieh MB, Li W, Lin Y, Singhal L, Iyer, MA, Pan DZ (2020) High-definition routing congestion prediction for large-scale fpgas. In: Proceedings of Asia and South Pacific Design Automation Conference, pp 26–31 . IEEE

  26. Odena A, Dumoulin V, Olah C (2016) Deconvolution and checkerboard artifacts. Distill. https://doi.org/10.23915/distill.00003

  27. Bustany IS, Chinnery D, Shinnerl JR, Yutsis V (2015) Ispd 2015 benchmarks with fence regions and routing blockages for detailed-routing-driven placement. In: Proceedings of the Symposium on International Symposium on Physical Design, pp 157–164

  28. Darav NK, Bustany IS, Kennings A, Mamidi R (2017) Iccad-2017 cad contest in multi-deck standard cell legalization and benchmarks. In: Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 867–871. IEEE

  29. Dolgov S, Volkov A, Wang L, Xu B (2019) 2019 cad contest: Lef/def based global routing. In: Proceedings of the IEEE/ACM International Conference on Computer-aided Design, pp 1–4 . IEEE

  30. Zhu W, Huang Z, Chen J, Chang Y-W (2018) Analytical solution of Poisson’s equation and its application to vlsi global placement. In: Proceedings of the International Conference on Computer-aided Design, pp 1–8

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Authors and Affiliations

  1. The Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, 350108, China

    Yilu Chen & Xiqiong Bai

  2. The School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350108, China

    Miaodi Su & Zhifeng Lin

  3. The College of Computer and Data Science, Fuzhou University, Fuzhou, 350108, China

    Hongzhi Ding & Shaohong Weng

Authors
  1. Yilu Chen
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  2. Miaodi Su
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  3. Hongzhi Ding
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  4. Shaohong Weng
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  5. Zhifeng Lin
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  6. Xiqiong Bai
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Contributions

YC, MS and XB gave the idea and wrote the main manuscript text. HD, SW and ZL did the experiments. All authors reviewed the manuscript.

Corresponding author

Correspondence to Xiqiong Bai.

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Preliminary version of this paper was presented at the 2022 Asia and South Pacific Design Automation Conference, ASP-DAC, Taipei, Taiwan, January 17-20, 2022 [22].

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Chen, Y., Su, M., Ding, H. et al. High-correlation 3D routability estimation for congestion-guided global routing. J Supercomput 80, 3114–3141 (2024). https://doi.org/10.1007/s11227-023-05553-0

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