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Massively Parallel Ruling Set Made Deterministic

Authors Jeff Giliberti , Zahra Parsaeian

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ACM Subject Classification
  • Theory of computation → MapReduce algorithms
Keywords
  • deterministic algorithms
  • distributed computing
  • massively parallel computation
  • graph algorithms
  • derandomization

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Abstract

We study the deterministic complexity of the 2-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory.
- Linear MPC: We present a constant-round deterministic algorithm for the 2-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic O(log log n)-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU’s algorithm based solely on bounded independence, which makes its efficient derandomization possible.
- Sublinear MPC: We present a deterministic algorithm that computes a 2-Ruling Set in Õ(√{log n}) rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the O(log Δ + log log^* n)-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized Õ(√{log n})-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12].

Cite As Get BibTex

Jeff Giliberti and Zahra Parsaeian. Massively Parallel Ruling Set Made Deterministic. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.29

Author Details

Jeff Giliberti
  • University of Maryland, College Park, MD, USA
Zahra Parsaeian
  • University of Freiburg, Germany

Funding

  • Giliberti, Jeff: Financial support in part by the Fulbright U.S. Graduate Student Program, sponsored by the U.S. Department of State and the Italian-American Fulbright Commission. The content does not necessarily represent the views of the Program.

Acknowledgements

We are grateful to Christoph Grunau and Manuela Fischer for valuable discussions. We would also like to thank the anonymous reviewers for their helpful feedback, and Yannic Maus for his shepherding of the paper.

References

  1. Noga Alon, László Babai, and Alon Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms, 7(4):567-583, 1986. URL: https://doi.org/10.1016/0196-6774(86)90019-2.
  2. Alexandr Andoni, Aleksandar Nikolov, Krzysztof Onak, and Grigory Yaroslavtsev. Parallel algorithms for geometric graph problems. Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2013. URL: https://api.semanticscholar.org/CorpusID:316401.
  3. Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. Lower bounds for maximal matchings and maximal independent sets. 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), pages 481-497, 2019. URL: https://api.semanticscholar.org/CorpusID:57721262.
  4. Alkida Balliu, Sebastian Brandt, Fabian Kuhn, and Dennis Olivetti. Distributed delta-coloring plays hide-and-seek. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, pages 464-477, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3519935.3520027.
  5. Alkida Balliu, Sebastian Brandt, and Dennis Olivetti. Distributed lower bounds for ruling sets. SIAM Journal on Computing, pages 70-115, 2022. URL: https://epubs.siam.org/doi/10.1137/20M1381770, URL: https://doi.org/10.1137/20M1381770.
  6. Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. The locality of distributed symmetry breaking. J. ACM, 63(3), June 2016. URL: https://doi.org/10.1145/2903137.
  7. Paul Beame, Paraschos Koutris, and Dan Suciu. Communication steps for parallel query processing. Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI symposium on Principles of database systems, 2013. URL: https://api.semanticscholar.org/CorpusID:11086753.
  8. M. Bellare and J. Rompel. Randomness-efficient oblivious sampling. In Proceedings 35th Annual Symposium on Foundations of Computer Science, pages 276-287, 1994. URL: https://doi.org/10.1109/SFCS.1994.365687.
  9. Andrew Berns, James Hegeman, and Sriram V. Pemmaraju. Super-fast distributed algorithms for metric facility location. ArXiv, abs/1308.2473, 2012. URL: https://api.semanticscholar.org/CorpusID:124685, URL: https://arxiv.org/abs/1308.2473.
  10. Tushar Bisht, Kishore Kothapalli, and Sriram V. Pemmaraju. Brief announcement: Super-fast t-ruling sets. Proceedings of the 2014 ACM symposium on Principles of distributed computing, 2014. URL: https://api.semanticscholar.org/CorpusID:12210091.
  11. Mélanie Cambus, Fabian Kuhn, Shreyas Pai, and Jara Uitto. Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem. In Rotem Oshman, editor, 37th International Symposium on Distributed Computing (DISC 2023), volume 281 of Leibniz International Proceedings in Informatics (LIPIcs), pages 11:1-11:12, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2023.11.
  12. Keren Censor-Hillel, Merav Parter, and Gregory Schwartzman. Derandomizing local distributed algorithms under bandwidth restrictions. Distributed Computing, 33(3):349-366, June 2020. URL: https://doi.org/10.1007/s00446-020-00376-1.
  13. Yi-Jun Chang, Manuela Fischer, Mohsen Ghaffari, Jara Uitto, and Yufan Zheng. The Complexity of (Delta+1) Coloring in Congested Clique, Massively Parallel Computation, and Centralized Local Computation. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC '19, pages 471-480, New York, NY, USA, 2019. Association for Computing Machinery. URL: https://doi.org/10.1145/3293611.3331607.
  14. Benny Chor and Oded Goldreich. On the power of two-point based sampling. Journal of Complexity, 5(1):96-106, 1989. URL: https://doi.org/10.1016/0885-064X(89)90015-0.
  15. Sam Coy and Artur Czumaj. Deterministic massively parallel connectivity. In Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022, pages 162-175, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3519935.3520055.
  16. Artur Czumaj, Peter Davies, and Merav Parter. Simple, deterministic, constant-round coloring in the congested clique. In Proceedings of the 39th Symposium on Principles of Distributed Computing, PODC '20, pages 309-318, New York, NY, USA, 2020. Association for Computing Machinery. URL: https://doi.org/10.1145/3382734.3405751.
  17. Artur Czumaj, Peter Davies, and Merav Parter. Component stability in low-space massively parallel computation. In Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, PODC'21, pages 481-491, New York, NY, USA, 2021. Association for Computing Machinery. URL: https://doi.org/10.1145/3465084.3467903.
  18. Artur Czumaj, Peter Davies, and Merav Parter. Graph sparsification for derandomizing massively parallel computation with low space. ACM Trans. Algorithms, 17(2), May 2021. URL: https://doi.org/10.1145/3451992.
  19. Artur Czumaj, Peter Davies, and Merav Parter. Improved Deterministic (Delta+1) Coloring in Low-Space MPC. In Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, PODC'21, pages 469-479, New York, NY, USA, 2021. Association for Computing Machinery. URL: https://doi.org/10.1145/3465084.3467937.
  20. Artur Czumaj, Peter Davies-Peck, and Merav Parter. Component stability in low-space massively parallel computation. Distributed Computing, 37(1):35-64, March 2024. URL: https://doi.org/10.1007/s00446-024-00461-9.
  21. Guy Even, Oded Goldreich, Michael Luby, Noam Nisan, and Boban Veličković. Efficient approximation of product distributions. Random Structures & Algorithms, 13(1):1-16, 1998. URL: https://doi.org/10.1002/(SICI)1098-2418(199808)13:1<1::AID-RSA1>3.0.CO;2-W.
  22. Manuela Fischer, Jeff Giliberti, and Christoph Grunau. Improved Deterministic Connectivity in Massively Parallel Computation. In Christian Scheideler, editor, 36th International Symposium on Distributed Computing (DISC 2022), volume 246 of Leibniz International Proceedings in Informatics (LIPIcs), pages 22:1-22:17, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.DISC.2022.22.
  23. Manuela Fischer, Jeff Giliberti, and Christoph Grunau. Deterministic massively parallel symmetry breaking for sparse graphs. In Proceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '23, pages 89-100, New York, NY, USA, 2023. Association for Computing Machinery. URL: https://doi.org/10.1145/3558481.3591081.
  24. Beat Gfeller and Elias Vicari. A randomized distributed algorithm for the maximal independent set problem in growth-bounded graphs. In ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, 2007. URL: https://api.semanticscholar.org/CorpusID:13473182.
  25. Mohsen Ghaffari. An improved distributed algorithm for maximal independent set. In Proceedings of the 2016 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 270-277, 2016. URL: https://doi.org/10.1137/1.9781611974331.ch20.
  26. Mohsen Ghaffari, Themis Gouleakis, Christian Konrad, Slobodan Mitrović, and Ronitt Rubinfeld. Improved massively parallel computation algorithms for mis, matching, and vertex cover. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC '18, pages 129-138, New York, NY, USA, 2018. Association for Computing Machinery. URL: https://doi.org/10.1145/3212734.3212743.
  27. Mohsen Ghaffari, Fabian Kuhn, and Jara Uitto. Conditional hardness results for massively parallel computation from distributed lower bounds. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), pages 1650-1663, 2019. URL: https://doi.org/10.1109/FOCS.2019.00097.
  28. Mohsen Ghaffari and Jara Uitto. Sparsifying distributed algorithms with ramifications in massively parallel computation and centralized local computation. In Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1636-1653, 2019. URL: https://doi.org/10.1137/1.9781611975482.99.
  29. Michael T. Goodrich. Communication-efficient parallel sorting. SIAM Journal on Computing, 29(2):416-432, 1999. URL: https://doi.org/10.1137/S0097539795294141.
  30. Michael T. Goodrich, Nodari Sitchinava, and Qin Zhang. Sorting, searching, and simulation in the mapreduce framework. In Takao Asano, Shin-ichi Nakano, Yoshio Okamoto, and Osamu Watanabe, editors, Algorithms and Computation, pages 374-383, Berlin, Heidelberg, 2011. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-25591-5_39.
  31. James Hegeman, Sriram V. Pemmaraju, and Vivek Sardeshmukh. Near-constant-time distributed algorithms on a congested clique. In International Symposium on Distributed Computing, 2014. URL: https://api.semanticscholar.org/CorpusID:277941.
  32. Howard Karloff, Siddharth Suri, and Sergei Vassilvitskii. A model of computation for mapreduce. In Proceedings of the 2010 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 938-948, 2010. URL: https://doi.org/10.1137/1.9781611973075.76.
  33. Kishore Kothapalli, Shreyas Pai, and Sriram V. Pemmaraju. Sample-And-Gather: Fast Ruling Set Algorithms in the Low-Memory MPC Model. In Nitin Saxena and Sunil Simon, editors, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020), volume 182 of Leibniz International Proceedings in Informatics (LIPIcs), pages 28:1-28:18, Dagstuhl, Germany, 2020. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.FSTTCS.2020.28.
  34. Kishore Kothapalli and Sriram Pemmaraju. Distributed graph coloring in a few rounds. In Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC '11, pages 31-40, New York, NY, USA, 2011. Association for Computing Machinery. URL: https://doi.org/10.1145/1993806.1993812.
  35. Kishore Kothapalli and Sriram V. Pemmaraju. Super-fast 3-ruling sets. In Foundations of Software Technology and Theoretical Computer Science, 2012. URL: https://api.semanticscholar.org/CorpusID:16038481.
  36. Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Local computation: Lower and upper bounds. J. ACM, 63(2), 2016. URL: https://doi.org/10.1145/2742012.
  37. Nathan Linial. Locality in distributed graph algorithms. SIAM Journal on Computing, 21(1):193-201, 1992. URL: https://doi.org/10.1137/0221015.
  38. Michael Luby. Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993. URL: https://doi.org/10.1016/0022-0000(93)90033-S.
  39. Yannic Maus, Saku Peltonen, and Jara Uitto. Distributed symmetry breaking on power graphs via sparsification. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC '23, pages 157-167, New York, NY, USA, 2023. Association for Computing Machinery. URL: https://doi.org/10.1145/3583668.3594579.
  40. Rajeev Motwani and Prabhakar Raghavan. Randomized algorithms. Cambridge university press, 1995. URL: https://doi.org/10.1017/CBO9780511814075.
  41. Rajeev Motwani, Joseph (Seffi) Naor, and Moni Naor. The probabilistic method yields deterministic parallel algorithms. Journal of Computer and System Sciences, 49(3):478-516, 1994. 30th IEEE Conference on Foundations of Computer Science. URL: https://doi.org/10.1016/S0022-0000(05)80069-8.
  42. Krzysztof Nowicki. A deterministic algorithm for the mst problem in constant rounds of congested clique. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pages 1154-1165, New York, NY, USA, 2021. Association for Computing Machinery. URL: https://doi.org/10.1145/3406325.3451136.
  43. Shreyas Pai and Sriram V. Pemmaraju. Brief announcement: Deterministic massively parallel algorithms for ruling sets. In Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing, PODC'22, pages 366-368, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3519270.3538472.
  44. Prabhakar Raghavan. Probabilistic construction of deterministic algorithms: Approximating packing integer programs. Journal of Computer and System Sciences, 37(2):130-143, 1988. URL: https://doi.org/10.1016/0022-0000(88)90003-7.
  45. Johannes Schneider, Michael Elkin, and Roger Wattenhofer. Symmetry breaking depending on the chromatic number or the neighborhood growth. Theor. Comput. Sci., 509:40-50, 2013. URL: https://doi.org/10.1016/J.TCS.2012.09.004.
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