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Neither Cover nor Pack: Distributed Worst-Case Optimality of Degree-2 Joins

Authors Heba Aamer , Xiao Hu , Bas Ketsman

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Logic and databases
  • Theory of computation → Abstract machines
Keywords
  • degree-two joins
  • worst-case optimality
  • distributed algorithms

Metrics

Abstract

We study the worst-case communication complexity of the join query evaluation problem over large-scale data in distributed shared-nothing systems under the MPC model. We focus on multi-round MPC algorithms that run in constant number of rounds. The problem is well-understood for a few classes of queries, mainly the class of acyclic queries and the class of graph-like queries. For queries not belonging to either class, the complexity picture is much less clear. We study the class of degree-two queries and fragments thereof. In this paper, we tighten the gap between the upper and lower bounds for the studied classes and establish worst-case optimality for some fragments of the considered classes. We also debunk a well-believed conjecture about which query-related quantity, in the worst-case, optimally captures the communication complexity of the studied problem.

Cite As Get BibTex

Heba Aamer, Xiao Hu, and Bas Ketsman. Neither Cover nor Pack: Distributed Worst-Case Optimality of Degree-2 Joins. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICDT.2026.8

Author Details

Heba Aamer
  • Vrije Universiteit Brussel, Belgium
Xiao Hu
  • University of Waterloo, Canada
Bas Ketsman
  • Vrije Universiteit Brussel, Belgium

Funding

This work is partially funded by FWO-grant G062721N.
  • Aamer, Heba: The work of Heba Aamer is fully funded by FWO-grant 1210525N.

References

  1. Heba Aamer and Bas Ketsman. PAC: Computing Join Queries with Semi-Covers. In Sudeepa Roy and Ahmet Kara, editors, 28th International Conference on Database Theory (ICDT 2025), volume 328 of Leibniz International Proceedings in Informatics (LIPIcs), pages 6:1-6:20, Dagstuhl, Germany, 2025. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICDT.2025.6.
  2. Foto N. Afrati and Jeffrey D. Ullman. Optimizing multiway joins in a map-reduce environment. IEEE Trans. Knowl. Data Eng., 23(9):1282-1298, 2011. URL: https://doi.org/10.1109/TKDE.2011.47.
  3. Paul Beame, Paraschos Koutris, and Dan Suciu. Communication steps for parallel query processing. In Richard Hull and Wenfei Fan, editors, Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2013, New York, NY, USA, 2013, pages 273-284. ACM, 2013. URL: https://doi.org/10.1145/2463664.2465224.
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  5. Xiao Hu. Cover or pack: New upper and lower bounds for massively parallel joins. In Leonid Libkin, Reinhard Pichler, and Paolo Guagliardo, editors, PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, 2021, pages 181-198. ACM, 2021. URL: https://doi.org/10.1145/3452021.3458319.
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  9. Bas Ketsman, Dan Suciu, and Yufei Tao. A near-optimal parallel algorithm for joining binary relations. Log. Methods Comput. Sci., 18(2), 2022. URL: https://doi.org/10.46298/lmcs-18(2:6)2022.
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