Startseite The power of locality: Exploring the limits of randomness in distributed computing
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

The power of locality: Exploring the limits of randomness in distributed computing

  • Yannic Maus

    Dr. Yannic Maus studied Mathematics and Computer Science at the RWTH Aachen University and the National University of Singapore where he received the Springorum-Denkmünze RWTH Aachen University Award for his studies. After his master studies he pursued a PhD from the Albert-Ludwigs-Universität Freiburg under the supervision of Professor Dr. Fabian Kuhn and in October 2018 he graduated summa cum laude in the area of distributed graph algorithms. For his dissertation he received the dissertation award of the German Informatics Society 2018 and the 2019 Wolfgang-Gentner Award for the Promotion of Young Scientists. Afterwards he moved to the country with the largest density of excellent researchers in the area of distributed algorithms, that is, he moved to the Technion () in Haifa, Israel , where he works as a postdoctoral researcher in the group of Professor Dr. Keren Censor-Hillel. In his leisure time he loves riding his (road) bike or the joys of cross country skiing.

    EMAIL logo
Veröffentlicht/Copyright: 21. Januar 2020

Abstract

Many modern systems are built on top of large-scale networks like the Internet. This article provides an overview of a dissertation [29] that addresses the complexity of classic graph problems like the vertex coloring problem in such networks. It has been known for a long time that randomization helps significantly in solving many of these problems, whereas the best known deterministic algorithms have been exponentially slower. In the first part of the dissertation we use a complexity theoretic approach to show that several problems are complete in the following sense: An efficient deterministic algorithm for any complete problem would imply an efficient algorithm for all problems that can be solved efficiently with a randomized algorithm. Among the complete problems is a rudimentary looking graph coloring problem that can be solved by a randomized algorithm without any communication. In further parts of the dissertation we develop efficient distributed algorithms for several problems where the most important problems are distributed versions of integer linear programs, the vertex coloring problem and the edge coloring problem. We also prove a lower bound on the runtime of any deterministic algorithm that solves the vertex coloring problem in a weak variant of the standard model of the area.

ACM CCS:

Article note

The dissertation of Dr. Yannic Maus has received the GI Dissertation Award 2018 and the 2019 Wolfgang-Gentner Award for the Promotion of Young Scientists.


About the author

Yannic Maus

Dr. Yannic Maus studied Mathematics and Computer Science at the RWTH Aachen University and the National University of Singapore where he received the Springorum-Denkmünze RWTH Aachen University Award for his studies. After his master studies he pursued a PhD from the Albert-Ludwigs-Universität Freiburg under the supervision of Professor Dr. Fabian Kuhn and in October 2018 he graduated summa cum laude in the area of distributed graph algorithms. For his dissertation he received the dissertation award of the German Informatics Society 2018 and the 2019 Wolfgang-Gentner Award for the Promotion of Young Scientists. Afterwards he moved to the country with the largest density of excellent researchers in the area of distributed algorithms, that is, he moved to the Technion () in Haifa, Israel , where he works as a postdoctoral researcher in the group of Professor Dr. Keren Censor-Hillel. In his leisure time he loves riding his (road) bike or the joys of cross country skiing.

References

1. N. Alon, L. Babai, and A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7(4):567–583, 1986.10.1016/0196-6774(86)90019-2Suche in Google Scholar

2. B. Awerbuch, A. V. Goldberg, M. Luby, and S. A. Plotkin. Network decomposition and locality in distributed computation. In Proceedings of the Symposium on Foundations of Computer Science (FOCS), pages 364–369, 1989.10.1109/SFCS.1989.63504Suche in Google Scholar

3. P. Bamberger, M. Ghaffari, F. Kuhn, Y. Maus, and J. Uitto. On the complexity of distributed splitting problems. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 – August 2, 2019, pages 280–289, 2019.10.1145/3293611.3331630Suche in Google Scholar

4. L. Barenboim and M. Elkin. Distributed Graph Coloring: Fundamentals and Recent Developments. Morgan & Claypool Publishers, 2013.10.2200/S00520ED1V01Y201307DCT011Suche in Google Scholar

5. S. Brandt, O. Fischer, J. Hirvonen, B. Keller, T. Lempiäinen, J. Rybicki, J. Suomela, and J. Uitto. A lower bound for the distributed lovász local lemma. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 479–488. ACM, 2016.10.1145/2897518.2897570Suche in Google Scholar

6. R. L. Brooks. On colouring the nodes of a network. Mathematical Proceedings of the Cambridge Philosophical Society, 37(2):194–197, 1941.10.1007/978-0-8176-4842-8_7Suche in Google Scholar

7. Y. J. Chang, T. Kopelowitz, and S. Pettie. An exponential separation between randomized and deterministic complexity in the local model. In Proceedings of the Symposium on Foundations of Computer Science (FOCS), pages 615–624, 2016.10.1109/FOCS.2016.72Suche in Google Scholar

8. Y.-J. Chang, W. Li, and S. Pettie. An optimal distributed (Δ + 1)-coloring algorithm? In Proceedings of the ACM Symposium on Theory of Computing (STOC), 2018.10.1145/3188745.3188964Suche in Google Scholar

9. M. Fischer, M. Ghaffari, and F. Kuhn. Deterministic distributed edge-coloring via hypergraph maximal matching. In Proceedings of the Symposium on Foundations of Computer Science (FOCS), pages 180–191. IEEE Computer Society, 2017.10.1109/FOCS.2017.25Suche in Google Scholar

10. P. Fraigniaud, A. Korman, and D. Peleg. Towards a complexity theory for local distributed computing. Journal of the ACM, 60(5):35, 2013.10.1145/2499228Suche in Google Scholar

11. M. Ghaffari. An improved distributed algorithm for maximal independent set. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 270–277, 2016.10.1137/1.9781611974331.ch20Suche in Google Scholar

12. M. Ghaffari. Improved Distributed Algorithms for Fundamental Graph Problems. PhD thesis, MIT, USA, 2017.Suche in Google Scholar

13. M. Ghaffari, D. G. Harris, and F. Kuhn. On derandomizing local distributed algorithms. In Proc. Symp. on Foundations of Computer Science (FOCS), pages 662–673, 2018.10.1109/FOCS.2018.00069Suche in Google Scholar

14. M. Ghaffari, J. Hirvonen, F. Kuhn, and Y. Maus. Improved Distributed Δ-Coloring. In Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC), 2018.10.1145/3212734.3212764Suche in Google Scholar

15. M. Ghaffari, J. Hirvonen, F. Kuhn, Y. Maus, J. Suomela, and J. Uitto. Improved distributed degree splitting and edge coloring. In Proceedings of the International Symposium on Distributed Computing (DISC), pages 19:1–19:15, 2017.Suche in Google Scholar

16. M. Ghaffari, F. Kuhn, and Y. Maus. On the complexity of local distributed graph problems. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 784–797. ACM, 2017.10.1145/3055399.3055471Suche in Google Scholar

17. M. Ghaffari, F. Kuhn, Y. Maus, and Jara Uitto. Deterministic distributed edge-coloring with fewer colors. In Proceedings of the ACM Symposium on Theory of Computing (STOC). ACM, 2018.10.1145/3188745.3188906Suche in Google Scholar

18. M. Ghaffari and H.-H. Su. Distributed degree splitting, edge coloring, and orientations. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2505–2523, 2017.10.1137/1.9781611974782.166Suche in Google Scholar

19. M. Hańćkowiak, M. Karoński, and A. Panconesi. On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics, 15(1):41–57, 2001.10.1137/S0895480100373121Suche in Google Scholar

20. S. G. Harris, J. Schneider, and H.-H. Su. Distributed (Δ + 1)-coloring in sublogarithmic rounds. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 2016.10.1145/2897518.2897533Suche in Google Scholar

21. D. Hefetz, Y. Maus, F. Kuhn, and A. Steger. A polynomial lower bound for distributed graph coloring in a weak LOCAL model. In Proceedings of the International Symposium on Distributed Computing (DISC), pages 99–113, 2016.10.1007/978-3-662-53426-7_8Suche in Google Scholar

22. R. M. Karp. Reducibility among combinatorial problems. In Symposium on Complexity of Computer Computations, pages 85–103, 1972.10.1007/978-1-4684-2001-2_9Suche in Google Scholar

23. D. R. Kowalski and P. Krysta. Deterministic coloring algorithms in the local model, 2019.Suche in Google Scholar

24. F. Kuhn. The price of locality: exploring the complexity of distributed coordination primitives. PhD thesis, ETH Zurich, 2005.Suche in Google Scholar

25. F. Kuhn, T. Moscibroda, and R. Wattenhofer. The price of being near-sighted. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 980–989, 2006.10.1145/1109557.1109666Suche in Google Scholar

26. N. Linial. Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1):193–201, 1992.10.1137/0221015Suche in Google Scholar

27. N. Linial and M. Saks. Low diameter graph decompositions. Combinatorica, 13(4):441–454, 1993.10.1007/BF01303516Suche in Google Scholar

28. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing, 15(4):1036–1053, 1986.10.1145/22145.22146Suche in Google Scholar

29. Y. Maus. The power of locality: exploring the limits of randomness in distributed computing. PhD thesis, University of Freiburg, Freiburg im Breisgau, Germany, 2018.Suche in Google Scholar

30. M. Naor and L. Stockmeyer. What can be computed locally? SIAM Journal on Computing, 24(6):1259–1277, 1995.10.1145/167088.167149Suche in Google Scholar

31. A. Panconesi and R. Rizzi. Some simple distributed algorithms for sparse networks. Distributed Computing, 14(2):97–100, 2001.10.1007/PL00008932Suche in Google Scholar

32. A. Panconesi and A. Srinivasan. Improved distributed algorithms for coloring and network decomposition problems. In Proceedings of the ACM Symposium on Theory of Computing (STOC), pages 581–592. ACM, 1992.10.1145/129712.129769Suche in Google Scholar

33. A. Panconesi and A. Srinivasan. The local nature of Δ-coloring and its algorithmic applications. Combinatorica, 15(2):255–280, Jun 1995.10.1007/BF01200759Suche in Google Scholar

34. A. Panconesi and A. Srinivasan. On the complexity of distributed network decomposition. Journal of Algorithms, 20(2):581–592, 1995.10.1006/jagm.1996.0017Suche in Google Scholar

35. V. Rozhoň and M. Ghaffari. Polylogarithmic-time deterministic network decomposition and distributed derandomization. CoRR, abs/1907.10937, 2019.10.1145/3357713.3384298Suche in Google Scholar

36. S. Smorodinsky. Conflict-Free Coloring and its Applications, pages 331–389. Springer Berlin Heidelberg, Berlin, Heidelberg, 2013.10.1007/978-3-642-41498-5_12Suche in Google Scholar

37. V. Vizing. On an estimate of the chromatic class of a p-graph. Diskret analiz, 3:25–30, 1964.Suche in Google Scholar

Received: 2019-12-17
Accepted: 2019-12-19
Published Online: 2020-01-21
Published in Print: 2020-12-16

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/itit-2019-0051/html
Button zum nach oben scrollen