Document Open Access Logo

Distance Computations in the Hybrid Network Model via Oracle Simulations

Authors Keren Censor-Hillel , Dean Leitersdorf, Volodymyr Polosukhin



PDF
Thumbnail PDF

File

LIPIcs.STACS.2021.21.pdf
  • Filesize: 0.94 MB
  • 19 pages

Document Identifiers

Author Details

Keren Censor-Hillel
  • Technion - Israel Institute of Technology, Haifa, Israel
Dean Leitersdorf
  • Technion - Israel Institute of Technology, Haifa, Israel
Volodymyr Polosukhin
  • Technion - Israel Institute of Technology, Haifa, Israel

Acknowledgements

The authors would like to thank Michal Dory and Yuval Efron for various helpful conversations. We also thank Fabian Kuhn for sharing a preprint of [Kuhn and Schneider, 2020] with us.

Cite AsGet BibTex

Keren Censor-Hillel, Dean Leitersdorf, and Volodymyr Polosukhin. Distance Computations in the Hybrid Network Model via Oracle Simulations. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.21

Abstract

The Hybrid network model was introduced in [Augustine et al., SODA '20] for laying down a theoretical foundation for networks which combine two possible modes of communication: One mode allows high-bandwidth communication with neighboring nodes, and the other allows low-bandwidth communication over few long-range connections at a time. This fundamentally abstracts networks such as hybrid data centers, and class-based software-defined networks. Our technical contribution is a density-aware approach that allows us to simulate a set of oracles for an overlay skeleton graph over a Hybrid network. As applications of our oracle simulations, with additional machinery that we provide, we derive fast algorithms for fundamental distance-related tasks. One of our core contributions is an algorithm in the Hybrid model for computing exact weighted shortest paths from Õ(n^{1/3}) sources which completes in Õ(n^{1/3}) rounds w.h.p. This improves, in both the runtime and the number of sources, upon the algorithm of [Kuhn and Schneider, PODC ’20], which computes shortest paths from a single source in Õ(n^{2/5}) rounds w.h.p. We additionally show a 2-approximation for weighted diameter and a (1+ε)-approximation for unweighted diameter, both in Õ(n^{1/3}) rounds w.h.p., which is comparable to the ̃ Ω(n^{1/3}) lower bound of [Kuhn and Schneider, PODC ’20] for a (2-ε)-approximation for weighted diameter and an exact unweighted diameter. We also provide fast distance approximations from multiple sources and fast approximations for eccentricities.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed graph algorithms
  • Hybrid network model
  • Distance computations

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Amir Abboud, Keren Censor-Hillel, and Seri Khoury. Near-linear lower bounds for distributed distance computations, even in sparse networks. In Cyril Gavoille and David Ilcinkas, editors, Distributed Computing - 30th International Symposium, DISC 2016, Paris, France, September 27-29, 2016. Proceedings, volume 9888 of Lecture Notes in Computer Science, pages 29-42. Springer, 2016. URL: https://doi.org/10.1007/978-3-662-53426-7_3.
  2. Yehuda Afek, Gad M. Landau, Baruch Schieber, and Moti Yung. The power of multimedia: Combining point-to-point and multiaccess networks. Inf. Comput., 84(1):97-118, 1990. URL: https://doi.org/10.1016/0890-5401(90)90035-G.
  3. Udit Agarwal and Vijaya Ramachandran. Distributed weighted all pairs shortest paths through pipelining. In 2019 IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019, Rio de Janeiro, Brazil, May 20-24, 2019, pages 23-32. IEEE, 2019. URL: https://doi.org/10.1109/IPDPS.2019.00014.
  4. Udit Agarwal and Vijaya Ramachandran. Faster deterministic all pairs shortest paths in congest model. In Christian Scheideler and Michael Spear, editors, SPAA '20: 32nd ACM Symposium on Parallelism in Algorithms and Architectures, Virtual Event, USA, July 15-17, 2020, pages 11-21. ACM, 2020. URL: https://doi.org/10.1145/3350755.3400256.
  5. Udit Agarwal, Vijaya Ramachandran, Valerie King, and Matteo Pontecorvi. A deterministic distributed algorithm for exact weighted all-pairs shortest paths in õ(n ^3/2 ) rounds. In Calvin Newport and Idit Keidar, editors, Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, July 23-27, 2018, pages 199-205. ACM, 2018. URL: https://doi.org/10.1145/3212734.3212773.
  6. Bertie Ancona, Keren Censor-Hillel, Mina Dalirrooyfard, Yuval Efron, and Virginia Vassilevska Williams. Distributed distance approximation. CoRR, abs/2011.05066, 2020. URL: http://arxiv.org/abs/2011.05066.
  7. Arash Asadi, Vincenzo Mancuso, and Rohit Gupta. An sdr-based experimental study of outband D2D communications. In 35th Annual IEEE International Conference on Computer Communications, INFOCOM 2016, San Francisco, CA, USA, April 10-14, 2016, pages 1-9. IEEE, 2016. URL: https://doi.org/10.1109/INFOCOM.2016.7524372.
  8. John Augustine, Mohsen Ghaffari, Robert Gmyr, Kristian Hinnenthal, Christian Scheideler, Fabian Kuhn, and Jason Li. Distributed computation in node-capacitated networks. In Christian Scheideler and Petra Berenbrink, editors, The 31st ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2019, Phoenix, AZ, USA, June 22-24, 2019, pages 69-79. ACM, 2019. URL: https://doi.org/10.1145/3323165.3323195.
  9. John Augustine, Kristian Hinnenthal, Fabian Kuhn, Christian Scheideler, and Philipp Schneider. Shortest paths in a hybrid network model. In Shuchi Chawla, editor, Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 1280-1299. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.78.
  10. Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-optimal approximate shortest paths and transshipment in distributed and streaming models. In Andréa W. Richa, editor, 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria, volume 91 of LIPIcs, pages 7:1-7:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.DISC.2017.7.
  11. Aaron Bernstein and Danupon Nanongkai. Distributed exact weighted all-pairs shortest paths in near-linear time. In Moses Charikar and Edith Cohen, editors, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, AZ, USA, June 23-26, 2019, pages 334-342. ACM, 2019. URL: https://doi.org/10.1145/3313276.3316326.
  12. Keren Censor-Hillel, Michal Dory, Janne H. Korhonen, and Dean Leitersdorf. Fast approximate shortest paths in the congested clique. In Peter Robinson and Faith Ellen, editors, Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 - August 2, 2019, pages 74-83. ACM, 2019. Google Scholar
  13. Keren Censor-Hillel, Michal Dory, Janne H. Korhonen, and Dean Leitersdorf. Fast approximate shortest paths in the congested clique. In Peter Robinson and Faith Ellen, editors, Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 - August 2, 2019, pages 74-83. ACM, 2019. Google Scholar
  14. Keren Censor-Hillel, Petteri Kaski, Janne H. Korhonen, Christoph Lenzen, Ami Paz, and Jukka Suomela. Algebraic methods in the congested clique. Distributed Comput., 32(6):461-478, 2019. URL: https://doi.org/10.1007/s00446-016-0270-2.
  15. Keren Censor-Hillel, Dean Leitersdorf, and Volodymyr Polosukhin. Distance computations in the hybrid network model via oracle simulations. CoRR, abs/2010.13831, 2020. URL: http://arxiv.org/abs/2010.13831.
  16. Keren Censor-Hillel, Dean Leitersdorf, and Elia Turner. Sparse matrix multiplication and triangle listing in the congested clique model. Theor. Comput. Sci., 809:45-60, 2020. URL: https://doi.org/10.1016/j.tcs.2019.11.006.
  17. Yong Cui, Hongyi Wang, and Xiuzhen Cheng. Channel allocation in wireless data center networks. In INFOCOM 2011. 30th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, 10-15 April 2011, Shanghai, China, pages 1395-1403. IEEE, 2011. URL: https://doi.org/10.1109/INFCOM.2011.5934925.
  18. Michal Dory and Merav Parter. Exponentially faster shortest paths in the congested clique. In Yuval Emek and Christian Cachin, editors, PODC '20: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, August 3-7, 2020, pages 59-68. ACM, 2020. URL: https://doi.org/10.1145/3382734.3405711.
  19. Michael Elkin. Distributed exact shortest paths in sublinear time. J. ACM, 67(3):15:1-15:36, 2020. URL: https://doi.org/10.1145/3387161.
  20. Michael Feldmann, Kristian Hinnenthal, and Christian Scheideler. Fast hybrid network algorithms for shortest paths in sparse graphs. CoRR, abs/2007.01191, 2020. URL: http://arxiv.org/abs/2007.01191.
  21. Sebastian Forster and Danupon Nanongkai. A faster distributed single-source shortest paths algorithm. In Mikkel Thorup, editor, 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, Paris, France, October 7-9, 2018, pages 686-697. IEEE Computer Society, 2018. URL: https://doi.org/10.1109/FOCS.2018.00071.
  22. Silvio Frischknecht, Stephan Holzer, and Roger Wattenhofer. Networks cannot compute their diameter in sublinear time. In Yuval Rabani, editor, Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17-19, 2012, pages 1150-1162. SIAM, 2012. URL: https://doi.org/10.1137/1.9781611973099.91.
  23. François Le Gall. Further algebraic algorithms in the congested clique model and applications to graph-theoretic problems. In Cyril Gavoille and David Ilcinkas, editors, Distributed Computing - 30th International Symposium, DISC 2016, Paris, France, September 27-29, 2016. Proceedings, volume 9888 of Lecture Notes in Computer Science, pages 57-70. Springer, 2016. URL: https://doi.org/10.1007/978-3-662-53426-7_5.
  24. Mohsen Ghaffari and Jason Li. Improved distributed algorithms for exact shortest paths. In Ilias Diakonikolas, David Kempe, and Monika Henzinger, editors, Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, pages 431-444. ACM, 2018. URL: https://doi.org/10.1145/3188745.3188948.
  25. Robert Gmyr, Kristian Hinnenthal, Christian Scheideler, and Christian Sohler. Distributed monitoring of network properties: The power of hybrid networks. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 137:1-137:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.137.
  26. Kai Han, Zhiming Hu, Jun Luo, and Liu Xiang. RUSH: routing and scheduling for hybrid data center networks. In 2015 IEEE Conference on Computer Communications, INFOCOM 2015, Kowloon, Hong Kong, April 26 - May 1, 2015, pages 415-423. IEEE, 2015. URL: https://doi.org/10.1109/INFOCOM.2015.7218407.
  27. Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In Daniel Wichs and Yishay Mansour, editors, Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, MA, USA, June 18-21, 2016, pages 489-498. ACM, 2016. URL: https://doi.org/10.1145/2897518.2897638.
  28. Stephan Holzer and Nathan Pinsker. Approximation of distances and shortest paths in the broadcast congest clique. In Emmanuelle Anceaume, Christian Cachin, and Maria Gradinariu Potop-Butucaru, editors, 19th International Conference on Principles of Distributed Systems, OPODIS 2015, December 14-17, 2015, Rennes, France, volume 46 of LIPIcs, pages 6:1-6:16. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2015. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2015.6.
  29. He Huang, Xiangke Liao, Shanshan Li, Shaoliang Peng, Xiaodong Liu, and Bin Lin. The architecture and traffic management of wireless collaborated hybrid data center network. In Dah Ming Chiu, Jia Wang, Paul Barford, and Srinivasan Seshan, editors, ACM SIGCOMM 2013 Conference, SIGCOMM'13, Hong Kong, China, August 12-16, 2013, pages 511-512. ACM, 2013. URL: https://doi.org/10.1145/2486001.2491724.
  30. Fabian Kuhn and Philipp Schneider. Computing shortest paths and diameter in the hybrid network model. In Yuval Emek and Christian Cachin, editors, PODC '20: ACM Symposium on Principles of Distributed Computing, Virtual Event, Italy, August 3-7, 2020, pages 109-118. ACM, 2020. URL: https://doi.org/10.1145/3382734.3405719.
  31. Christoph Lenzen. Optimal deterministic routing and sorting on the congested clique. In Panagiota Fatourou and Gadi Taubenfeld, editors, ACM Symposium on Principles of Distributed Computing, PODC '13, Montreal, QC, Canada, July 22-24, 2013, pages 42-50. ACM, 2013. URL: https://doi.org/10.1145/2484239.2501983.
  32. Christoph Lenzen and Boaz Patt-Shamir. Fast partial distance estimation and applications. In Chryssis Georgiou and Paul G. Spirakis, editors, Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 153-162. ACM, 2015. URL: https://doi.org/10.1145/2767386.2767398.
  33. Christoph Lenzen, Boaz Patt-Shamir, and David Peleg. Distributed distance computation and routing with small messages. Distributed Comput., 32(2):133-157, 2019. URL: https://doi.org/10.1007/s00446-018-0326-6.
  34. Christoph Lenzen and David Peleg. Efficient distributed source detection with limited bandwidth. In Panagiota Fatourou and Gadi Taubenfeld, editors, ACM Symposium on Principles of Distributed Computing, PODC '13, Montreal, QC, Canada, July 22-24, 2013, pages 375-382. ACM, 2013. URL: https://doi.org/10.1145/2484239.2484262.
  35. Danupon Nanongkai. Distributed approximation algorithms for weighted shortest paths. In David B. Shmoys, editor, Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 565-573. ACM, 2014. URL: https://doi.org/10.1145/2591796.2591850.
  36. David Peleg, Liam Roditty, and Elad Tal. Distributed algorithms for network diameter and girth. In Artur Czumaj, Kurt Mehlhorn, Andrew M. Pitts, and Roger Wattenhofer, editors, Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part II, volume 7392 of Lecture Notes in Computer Science, pages 660-672. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-31585-5_58.
  37. Liam Roditty and Uri Zwick. On dynamic shortest paths problems. Algorithmica, 61(2):389-401, 2011. URL: https://doi.org/10.1007/s00453-010-9401-5.
  38. Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM J. Comput., 41(5):1235-1265, 2012. URL: https://doi.org/10.1137/11085178X.
  39. Jeffrey D. Ullman and Mihalis Yannakakis. High-probability parallel transitive-closure algorithms. SIAM J. Comput., 20(1):100-125, 1991. URL: https://doi.org/10.1137/0220006.
  40. Stefano Vissicchio, Laurent Vanbever, and Olivier Bonaventure. Opportunities and research challenges of hybrid software defined networks. Comput. Commun. Rev., 44(2):70-75, 2014. URL: https://doi.org/10.1145/2602204.2602216.
  41. Guohui Wang, David G. Andersen, Michael Kaminsky, Konstantina Papagiannaki, T. S. Eugene Ng, Michael Kozuch, and Michael P. Ryan. c-through: part-time optics in data centers. In Shivkumar Kalyanaraman, Venkata N. Padmanabhan, K. K. Ramakrishnan, Rajeev Shorey, and Geoffrey M. Voelker, editors, Proceedings of the ACM SIGCOMM 2010 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, New Delhi, India, August 30 -September 3, 2010, pages 327-338. ACM, 2010. URL: https://doi.org/10.1145/1851182.1851222.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail