Fast Deterministic Algorithms for Highly-Dynamic Networks

Authors Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, Gregory Schwartzman



PDF
Thumbnail PDF

File

LIPIcs.OPODIS.2020.28.pdf
  • Filesize: 0.49 MB
  • 16 pages

Document Identifiers

Author Details

Keren Censor-Hillel
  • Technion, Haifa, Israel
Neta Dafni
  • Technion, Haifa, Israel
Victor I. Kolobov
  • Technion, Haifa, Israel
Ami Paz
  • Faculty of Computer Science, Universität Wien, Austria
Gregory Schwartzman
  • Japan Advanced Institute of Science and Technology, Ishikawa, Japan

Acknowledgements

The authors are indebted to Yannic Maus for invaluable discussions which helped us pinpoint the exact definition of fixing in dynamic networks that we eventually use. We also thank Juho Hirvonen for comments about an earlier draft of this work, and Shay Solomon for useful discussions about his work in [Sepehr Assadi et al., 2018; Sepehr Assadi et al., 2019]. We thank Hagit Attiya and Michal Dory for their input about related work.

Cite As Get BibTex

Keren Censor-Hillel, Neta Dafni, Victor I. Kolobov, Ami Paz, and Gregory Schwartzman. Fast Deterministic Algorithms for Highly-Dynamic Networks. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.OPODIS.2020.28

Abstract

This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which arbitrarily many edge changes may occur in each round. Our algorithm significantly improves upon prior work in its combination of (1) having an O(1) amortized time complexity, (2) using only O(log{n})-bit messages, (3) not posing any restrictions on the dynamic behavior of the environment, (4) being deterministic, (5) having strong guarantees for intermediate solutions, and (6) being applicable for a wide family of tasks.
The tasks for which we deduce such an algorithm are maximal matching, (degree+1)-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set (which is the most subtle case). For some of these tasks, node insertions can also be among the allowed topology changes, and for some of them also abrupt node deletions.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • dynamic distributed algorithms

Metrics

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

References

  1. Sepehr Assadi, Krzysztof Onak, Baruch Schieber, and Shay Solomon. Fully dynamic maximal independent set with sublinear update time. In STOC, 2018. Google Scholar
  2. Sepehr Assadi, Krzysztof Onak, Baruch Schieber, and Shay Solomon. Fully dynamic maximal independent set with sublinear in n update time. In SODA, 2019. Google Scholar
  3. Hagit Attiya, Danny Dolev, and Nir Shavit. Bounded polynomial randomized consensus. In PODC, 1989. Google Scholar
  4. Yossi Azar, Shay Kutten, and Boaz Patt-Shamir. Distributed error confinement. ACM Trans. Algorithms, 2010. Google Scholar
  5. Alkida Balliu, Sebastian Brandt, Dennis Olivetti, and Jukka Suomela. How much does randomness help with locally checkable problems? CoRR, abs/1902.06803, 2019. Google Scholar
  6. Alkida Balliu, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Dennis Olivetti, and Jukka Suomela. New classes of distributed time complexity. In STOC, 2018. Google Scholar
  7. Philipp Bamberger, Fabian Kuhn, and Yannic Maus. Local distributed algorithms in highly dynamic networks. In IPDPS, 2019. Google Scholar
  8. Leonid Barenboim and Michael Elkin. Distributed Graph Coloring: Fundamentals and Recent Developments. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2013. Google Scholar
  9. Leonid Barenboim, Michael Elkin, and Uri Goldenberg. Locally-iterative distributed (Δ+1)-coloring below szegedy-vishwanathan barrier, and applications to self-stabilization and to restricted-bandwidth models. In PODC, 2018. Google Scholar
  10. Soheil Behnezhad, Mahsa Derakhshan, Mohammadtaghi Hajiaghayi, Cliff Stein, and Madhu Sudan. Fully dynamic maximal independent set with polylogarithmic update time. FOCS, 2019. Google Scholar
  11. Sayan Bhattacharya, Deeparnab Chakrabarty, Monika Henzinger, and Danupon Nanongkai. Dynamic algorithms for graph coloring. In SODA, 2018. Google Scholar
  12. Matthias Bonne and Keren Censor-Hillel. Distributed detection of cliques in dynamic networks. In ICALP, 2019. Google Scholar
  13. Sebastian Brandt, Orr Fischer, Juho Hirvonen, Barbara Keller, Tuomo Lempiäinen, Joel Rybicki, Jukka Suomela, and Jara Uitto. A lower bound for the distributed lovász local lemma. In STOC, 2016. Google Scholar
  14. Sebastian Brandt, Juho Hirvonen, Janne H. Korhonen, Tuomo Lempiäinen, Patric R. J. Östergård, Christopher Purcell, Joel Rybicki, Jukka Suomela, and Przemyslaw Uznanski. LCL problems on grids. In PODC, 2017. Google Scholar
  15. Keren Censor-Hillel, Elad Haramaty, and Zohar S. Karnin. Optimal dynamic distributed MIS. In PODC, 2016. Google Scholar
  16. Keren Censor-Hillel, Victor I. Kolobov, and Gregory Schwartzman. Finding subgraphs in highly dynamic networks. In submission, 2020. Google Scholar
  17. Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. An exponential separation between randomized and deterministic complexity in the LOCAL model. SIAM J. Comput., 2019. Google Scholar
  18. Yi-Jun Chang and Seth Pettie. A time hierarchy theorem for the LOCAL model. SIAM J. Comput., 2019. Google Scholar
  19. Shiri Chechik and Tianyi Zhang. Fully dynamic maximal independent set in expected poly-log update time. FOCS, 2019. Google Scholar
  20. Shlomi Dolev. Self-Stabilization. MIT Press, 2000. Google Scholar
  21. Yuhao Du and Hengjie Zhang. Improved algorithms for fully dynamic maximal independent set. CoRR, abs/1804.08908, 2018. URL: http://arxiv.org/abs/1804.08908.
  22. Michael Elkin. A near-optimal distributed fully dynamic algorithm for maintaining sparse spanners. In PODC, 2007. Google Scholar
  23. Mohsen Ghaffari, Fabian Kuhn, and Yannic Maus. On the complexity of local distributed graph problems. In STOC, 2017. Google Scholar
  24. Nabil Guellati and Hamamache Kheddouci. A survey on self-stabilizing algorithms for independence, domination, coloring, and matching in graphs. J. Parallel Distrib. Comput., 2010. Google Scholar
  25. Manoj Gupta and Shahbaz Khan. Simple dynamic algorithms for maximal independent set and other problems. CoRR, abs/1804.01823, 2018. URL: http://arxiv.org/abs/1804.01823.
  26. Giuseppe F. Italiano. Distributed algorithms for updating shortest paths (extended abstract). In WDAG, 1991. Google Scholar
  27. Ken-ichi Kawarabayashi and Gregory Schwartzman. Adapting local sequential algorithms to the distributed setting. In DISC, 2018. Google Scholar
  28. Michael König and Roger Wattenhofer. On local fixing. In OPODIS, 2013. Google Scholar
  29. Fabian Kuhn, Nancy A. Lynch, and Rotem Oshman. Distributed computation in dynamic networks. In STOC, 2010. Google Scholar
  30. Shay Kutten and David Peleg. Fault-local distributed mending. J. Algorithms, 1999. Google Scholar
  31. Shay Kutten and David Peleg. Tight fault locality. SIAM J. Comput., 2000. Google Scholar
  32. Moni Naor and Larry J. Stockmeyer. What can be computed locally? SIAM J. Comput., 1995. Google Scholar
  33. Merav Parter, David Peleg, and Shay Solomon. Local-on-average distributed tasks. In SODA, 2016. Google Scholar
  34. Shay Solomon. Fully dynamic maximal matching in constant update time. In FOCS, 2016. Google Scholar
  35. Jukka Suomela. Survey of local algorithms. ACM Comput. Surv., 2013. Google Scholar
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