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Efficient Algorithms for Demand-Aware Networks and a Connection to Virtual Network Embedding

Authors Aleksander Figiel , Janne H. Korhonen, Neil Olver , Stefan Schmid

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Author Details

Aleksander Figiel
  • TU Berlin, Germany
Janne H. Korhonen
  • TU Berlin, Germany
Neil Olver
  • London School of Economics and Political Science, UK
Stefan Schmid
  • TU Berlin, Germany
  • Fraunhofer SIT, Berlin, Germany

Funding

This work is supported by the European Research Council (ERC) under grant agreement No. 864228 (AdjustNet), 2020-2025.

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Aleksander Figiel, Janne H. Korhonen, Neil Olver, and Stefan Schmid. Efficient Algorithms for Demand-Aware Networks and a Connection to Virtual Network Embedding. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 38:1-38:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.38

Abstract

Emerging optical switching technologies enable demand-aware datacenter networks, whose topology can be flexibly optimized toward the traffic they serve. This paper revisits the bounded-degree network design problem underlying such demand-aware networks. Namely, given a distribution over communicating node pairs (represented has a demand graph), we want to design a network with bounded maximum degree (called host graph) that minimizes the expected communication distance. 
We improve the understanding of this problem domain by filling several gaps in prior work. First, we present the first practical algorithm for solving this problem on arbitrary instances without violating the degree bound. Our algorithm is based on novel insights obtained from studying a new Steiner node version of the problem, and we report on an extensive empirical evaluation, using several real-world traffic traces from datacenters, finding that our approach results in improved demand-aware network designs. Second, we shed light on the complexity and hardness of the bounded-degree network design problem by formally establishing its NP-completeness for any degree. We use our techniques to improve prior upper bounds for sparse instances. 
Finally, we study an intriguing connection between demand-aware network design and the virtual networking embedding problem, and show that the latter cannot be used to approximate the former: there is no universal host graph which can provide a constant approximation for our problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • Networks → Data center networks
Keywords
  • demand-aware networks
  • algorithms
  • virtual network embedding

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References

  1. Vamsi Addanki, Chen Avin, and Stefan Schmid. Mars: Near-optimal throughput with shallow buffers in reconfigurable datacenter networks. Proc. ACM Meas. Anal. Comput. Syst., 7(1), March 2023. URL: https://doi.org/10.1145/3579312.
  2. Daniel Amir, Nitika Saran, Tegan Wilson, Robert Kleinberg, Vishal Shrivastav, and Hakim Weatherspoon. Shale: A practical, scalable oblivious reconfigurable network. In Proceedings of the ACM SIGCOMM 2024 Conference, ACM SIGCOMM '24, pages 449-464, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3651890.3672248.
  3. Daniel Amir, Tegan Wilson, Vishal Shrivastav, Hakim Weatherspoon, Robert Kleinberg, and Rachit Agarwal. Optimal oblivious reconfigurable networks. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, 2022. URL: https://doi.org/10.1145/3519935.3520020.
  4. Chen Avin, Manya Ghobadi, Chen Griner, and Stefan Schmid. On the complexity of traffic traces and implications. In Proc. ACM SIGMETRICS, 2020. Google Scholar
  5. Chen Avin, Manya Ghobadi, Chen Griner, and Stefan Schmid. On the complexity of traffic traces and implications. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 4(1):1-29, 2020. URL: https://doi.org/10.1145/3379486.
  6. Chen Avin, Alexandr Hercules, Andreas Loukas, and Stefan Schmid. rDAN: Toward robust demand-aware network designs. Information Processing Letters, 133:5-9, 2018. URL: https://doi.org/10.1016/J.IPL.2017.12.008.
  7. Chen Avin, Kaushik Mondal, and Stefan Schmid. Demand-aware network designs of bounded degree. In Proc. International Symposium on Distributed Computing (DISC), 2017. Google Scholar
  8. Chen Avin, Kaushik Mondal, and Stefan Schmid. Demand-aware network designs of bounded degree. Distributed Computing, 33(3):311-325, 2020. URL: https://doi.org/10.1007/S00446-019-00351-5.
  9. Chen Avin, Kaushik Mondal, and Stefan Schmid. Demand-aware network design with minimal congestion and route lengths. IEEE/ACM Transactions on Networking, 30(4):1838-1848, 2022. URL: https://doi.org/10.1109/TNET.2022.3153586.
  10. Chen Avin and Stefan Schmid. Renets: Statically-optimal demand-aware networks. In Symposium on Algorithmic Principles of Computer Systems (APOCS), pages 25-39. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976489.3.
  11. Chen Avin and Stefan Schmid. Renets: Statically-optimal demand-aware networks. In Proc. SIAM Symposium on Algorithmic Principles of Computer Systems (APOCS), 2021. Google Scholar
  12. Hitesh Ballani, Paolo Costa, Raphael Behrendt, Daniel Cletheroe, Istvan Haller, Krzysztof Jozwik, Fotini Karinou, Sophie Lange, Kai Shi, Benn Thomsen, et al. Sirius: A flat datacenter network with nanosecond optical switching. In Proceedings of the Annual conference of the ACM Special Interest Group on Data Communication on the applications, technologies, architectures, and protocols for computer communication, pages 782-797, 2020. Google Scholar
  13. Edward A Bender and E. Rodney Canfield. The asymptotic number of labeled graphs with given degree sequences. Journal of Combinatorial Theory, Series A, 24(3):296-307, 1978. URL: https://doi.org/10.1016/0097-3165(78)90059-6.
  14. NM Mosharaf Kabir Chowdhury, Muntasir Raihan Rahman, and Raouf Boutaba. Virtual network embedding with coordinated node and link mapping. In IEEE INFOCOM 2009, pages 783-791. IEEE, 2009. Google Scholar
  15. Thomas M. Cover and Joy A. Thomas. Elements of information theory. Wiley-Interscience, 2006. Google Scholar
  16. Fred Douglis, Seth Robertson, Eric Van den Berg, Josephine Micallef, Marc Pucci, Alex Aiken, Maarten Hattink, Mingoo Seok, and Keren Bergman. Fleet—fast lanes for expedited execution at 10 terabits: Program overview. IEEE Internet Computing, 25(3):79-87, 2021. URL: https://doi.org/10.1109/MIC.2021.3075326.
  17. Nathan Farrington and Alexey Andreyev. Facebook’s data center network architecture. In 2013 Optical Interconnects Conference, pages 49-50. IEEE, 2013. Google Scholar
  18. Aleksander Figiel, Leon Kellerhals, Rolf Niedermeier, Matthias Rost, Stefan Schmid, and Philipp Zschoche. Optimal virtual network embeddings for tree topologies. In Proceedings of the 33rd ACM Symposium on Parallelism in Algorithms and Architectures, pages 221-231, 2021. URL: https://doi.org/10.1145/3409964.3461787.
  19. Aleksander Figiel, Darya Melnyk, Andre Nichterlein, Arash Pourdamghani, and Stefan Schmid. Spiderdan: Matching augmentation in demand-aware networks. In SIAM Symposium on Algorithm Engineering and Experiments (ALENEX), 2025. Google Scholar
  20. M. R. Garey, D. S. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science, 1(3):237-267, 1976. URL: https://doi.org/10.1016/0304-3975(76)90059-1.
  21. Michael R. Garey and David S. Johnson. Computers and Intractability. W.H. Freeman and Company, 1979. Google Scholar
  22. Monia Ghobadi, Ratul Mahajan, Amar Phanishayee, Nikhil Devanur, Janardhan Kulkarni, Gireeja Ranade, Pierre-Alexandre Blanche, Houman Rastegarfar, Madeleine Glick, and Daniel Kilper. Projector: Agile reconfigurable data center interconnect. In Proceedings of the 2016 ACM SIGCOMM Conference, pages 216-229. ACM, 2016. URL: https://doi.org/10.1145/2934872.2934911.
  23. Chen Griner, Johannes Zerwas, Andreas Blenk, Manya Ghobadi, Stefan Schmid, and Chen Avin. Cerberus: The power of choices in datacenter topology design (a throughput perspective). Proc. ACM Meas. Anal. Comput. Syst., 5(3), December 2021. URL: https://doi.org/10.1145/3491050.
  24. Matthew Nance Hall, Klaus-Tycho Foerster, Stefan Schmid, and Ramakrishnan Durairajan. A survey of reconfigurable optical networks. Optical Switching and Networking, 41:100621, 2021. URL: https://doi.org/10.1016/J.OSN.2021.100621.
  25. Navid Hamedazimi, Zafar Qazi, Himanshu Gupta, Vyas Sekar, Samir R. Das, Jon P. Longtin, Himanshu Shah, and Ashish Tanwer. Firefly: a reconfigurable wireless data center fabric using free-space optics. SIGCOMM Comput. Commun. Rev., 44(4):319-330, August 2014. URL: https://doi.org/10.1145/2740070.2626328.
  26. Monika Henzinger, Stefan Neumann, and Stefan Schmid. Efficient distributed workload (re-) embedding. Proc. ACM SIGMETRICS, 2019. Google Scholar
  27. Stefan Höst. Information and Communication Theory. Wiley-IEEE Press, 2019. Google Scholar
  28. Wolfgang Kellerer, Patrick Kalmbach, Andreas Blenk, Arsany Basta, Martin Reisslein, and Stefan Schmid. Adaptable and data-driven softwarized networks: Review, opportunities, and challenges. Proceedings of the IEEE, 107(4):711-731, 2019. URL: https://doi.org/10.1109/JPROC.2019.2895553.
  29. Vincenzo Liberatore. Circular arrangements. In Proc. International Colloquium on Automata, Languages, and Programming (ICALP 2002), pages 1054-1065. Springer, 2002. URL: https://doi.org/10.1007/3-540-45465-9_90.
  30. Kurt Mehlhorn. Nearly optimal binary search trees. Acta Informatica, 5(4):287-295, 1975. URL: https://doi.org/10.1007/BF00264563.
  31. William M Mellette, Rajdeep Das, Yibo Guo, Rob McGuinness, Alex C Snoeren, and George Porter. Expanding across time to deliver bandwidth efficiency and low latency. In Proc. 17th USENIX Symposium on Networked Systems Design and Implementation (NSDI 20), pages 1-18, 2020. URL: https://www.usenix.org/conference/nsdi20/presentation/mellette.
  32. William M Mellette, Rob McGuinness, Arjun Roy, Alex Forencich, George Papen, Alex C Snoeren, and George Porter. Rotornet: A scalable, low-complexity, optical datacenter network. In Proceedings of the Conference of the ACM Special Interest Group on Data Communication, pages 267-280. ACM, 2017. URL: https://doi.org/10.1145/3098822.3098838.
  33. Alistair Moffat. Huffman coding. ACM Computing Surveys, 52(4), 2019. URL: https://doi.org/10.1145/3342555.
  34. Or Peres and Chen Avin. Distributed demand-aware network design using bounded square root of graphs. In IEEE Conference on Computer communications (INFOCOM). IEEE, 2023. URL: https://doi.org/10.1109/INFOCOM53939.2023.10228932.
  35. Arash Pourdamghani, Chen Avin, Robert Sama, Maryam Shiran, and Stefan Schmid. Hash & adjust: Competitive demand-aware consistent hashing. In International Conference on Principles of Distributed Systems (OPODIS), 2024. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2024.24.
  36. Leon Poutievski, Omid Mashayekhi, Joon Ong, Arjun Singh, Mukarram Tariq, Rui Wang, Jianan Zhang, Virginia Beauregard, Patrick Conner, Steve Gribble, et al. Jupiter evolving: transforming google’s datacenter network via optical circuit switches and software-defined networking. In Proc. ACM SIGCOMM 2022 Conference, pages 66-85, 2022. Google Scholar
  37. Matthias Rost and Stefan Schmid. Virtual network embedding approximations: Leveraging randomized rounding. IEEE/ACM Transactions on Networking, 27(5):2071-2084, 2019. URL: https://doi.org/10.1109/TNET.2019.2939950.
  38. D.D. Sleator and R.E. Tarjan. Self-adjusting binary search trees. Journal of the ACM (JACM), 32(3):652-686, 1985. URL: https://doi.org/10.1145/3828.3835.
  39. Min Yee Teh, Zhenguo Wu, and Keren Bergman. Flexspander: augmenting expander networks in high-performance systems with optical bandwidth steering. IEEE/OSA Journal of Optical Communications and Networking, 12(4):B44-B54, 2020. URL: https://doi.org/10.1364/JOCN.379487.
  40. Tegan Wilson, Daniel Amir, Nitika Saran, Robert Kleinberg, Vishal Shrivastav, and Hakim Weatherspoon. Breaking the vlb barrier for oblivious reconfigurable networks. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, 2024. URL: https://doi.org/10.1145/3618260.3649608.
  41. Johannes Zerwas, C Gyorgyi, A Blenk, Stefan Schmid, and Chen Avin. Duo: A high-throughput reconfigurable datacenter network using local routing and control. In Proc. ACM SIGMETRICS, 2023. Google Scholar
  42. Mingyang Zhang, Jianan Zhang, Rui Wang, Ramesh Govindan, Jeffrey C Mogul, and Amin Vahdat. Gemini: Practical reconfigurable datacenter networks with topology and traffic engineering. CoRR, 2021. URL: https://arxiv.org/abs/2110.08374.
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