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Estimating the cardinality of the output of a query is a fundamental problem in database query processing. In this article, we overview a recently published contribution that casts the cardinality estimation problem as linear optimization and computes guaranteed upper bounds on the cardinality of the output for any full conjunctive query. The objective of the linear program is to maximize the joint entropy of the query variables and its constraints are the Shannon information inequalities and new information inequalities involving ℓp-norms of the degree sequences of the join attributes. The bounds based on arbitrary norms can be asymptotically lower than those based on the ℓ1 and ℓ∞ norms, which capture the cardinalities and respectively the max-degrees of the input relations. They come with a matching query evaluation algorithm, are computable in exponential time in the query size, and are provably tight when each degree sequence is on one join attribute.
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Partition Constraints for Conjunctive Queries: Bounds and Worst-Case Optimal Joins
In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated statistics like functional dependencies and degree constraints. Each new statistic prompted work along two lines; bounding the size of conjunctive query outputs and worst-case optimal join algorithms. In this work, we continue in this vein by introducing a new statistic called a partition constraint. This statistic captures latent structure within relations by partitioning them into sub-relations which each have much tighter degree constraints. We show that this approach can both refine existing cardinality bounds and improve existing worst-case optimal join algorithms.
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- PAR ID:
- 10627053
- Editor(s):
- Roy, Sudeepa; Kara, Ahmet
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Volume:
- 328
- ISSN:
- 1868-8969
- ISBN:
- 978-3-95977-364-5
- Page Range / eLocation ID:
- 17:1-17:18
- Subject(s) / Keyword(s):
- Worst-Case Optimal Joins Cardinality Bounds Degeneracy Degree Constraints Partition Constraints Theory of computation → Database theory
- Format(s):
- Medium: X Size: 18 pages; 863108 bytes Other: application/pdf
- Size(s):
- 18 pages 863108 bytes
- Right(s):
- Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.4230/LIPICS.ICDT.2025.17
