research-article

On the Enumeration Complexity of Unions of Conjunctive Queries

Authors:

Markus KröllAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 46, Issue 2

Article No.: 5, Pages 1 - 41

https://doi.org/10.1145/3450263

Published: 29 May 2021 Publication History

Abstract

We study the enumeration complexity of Unions of Conjunctive Queries (UCQs). We aim to identify the UCQs that are tractable in the sense that the answer tuples can be enumerated with a linear preprocessing phase and a constant delay between every successive tuples. It has been established that, in the absence of self-joins and under conventional complexity assumptions, the CQs that admit such an evaluation are precisely the free-connex ones. A union of tractable CQs is always tractable. We generalize the notion of free-connexity from CQs to UCQs, thus showing that some unions containing intractable CQs are, in fact, tractable. Interestingly, some unions consisting of only intractable CQs are tractable too. We show how to use the techniques presented in this article also in settings where the database contains cardinality dependencies (including functional dependencies and key constraints) or when the UCQs contain disequalities. The question of finding a full characterization of the tractability of UCQs remains open. Nevertheless, we prove that, for several classes of queries, free-connexity fully captures the tractable UCQs.

References

[1]

Mahmoud Abo Khamis, Hung Q. Ngo, and Dan Suciu. 2017. What do Shannon-type inequalities, submodular width, and disjunctive datalog have to do with one another? In Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems. 429–444.

Digital Library

[2]

J. Alman and V. V. Williams. 2018. Limits on all known (and some unknown) approaches to matrix multiplication. In Proceedings of the 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS). 580–591.

[3]

N. Alon, R. Yuster, and U. Zwick. 1997. Finding and counting given length cycles. Algorithmica 17, 3 (1997), 209–223.

[4]

Guillaume Bagan, Arnaud Durand, and Etienne Grandjean. 2007. On acyclic conjunctive queries and constant delay enumeration. In Proceedings of the International Workshop on Computer Science Logic. Springer, 208–222.

[5]

Catriel Beeri, Ronald Fagin, David Maier, and Mihalis Yannakakis. 1983. On the desirability of acyclic database schemes. Journal of the ACM (JACM) 30, 3 (1983), 479–513.

Digital Library

[6]

Christoph Berkholz, Fabian Gerhardt, and Nicole Schweikardt. 2020. Constant delay enumeration for conjunctive queries: A tutorial. ACM SIGLOG News 7, 1 (2020), 4–33.

Digital Library

[7]

Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. 2017. Answering conjunctive queries under updates. In Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS 2017), (Chicago, IL, May 14-19, 2017). 303–318.

Digital Library

[8]

Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. 2018. Answering UCQs under updates and in the presence of integrity constraints. In Proceedings of the 21st International Conference on Database Theory (ICDT 2018), (March 26-29, 2018, Vienna, Austria). 8:1–8:19.

[9]

Johann Brault-Baron. 2013. De la pertinence de lâ énumération: Complexité en logiques propositionnelle et du premier ordre. Ph.D. Dissertation. Université de Caen.

[10]

Florent Capelli and Yann Strozecki. 2018. Incremental delay enumeration: Space and time. Discrete Applied Mathematics (2018).

[11]

Nofar Carmeli and Markus Kröll. 2019. Enumeration complexity of conjunctive queries with functional dependencies. Theory of Computing Systems (2019).

[12]

Nofar Carmeli and Markus Kröll. 2019. On the enumeration complexity of unions of conjunctive queries. In Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS 2019), Amsterdam, The Netherlands, June 30 - July 5, 2019, Dan Suciu, Sebastian Skritek, and Christoph Koch (Eds.). ACM, 134–148.

Digital Library

[13]

Ashok K. Chandra and Philip M. Merlin. 1977. Optimal implementation of conjunctive queries in relational data bases. In Proceedings of the 9th Annual ACM Symposium on Theory of Computing (STOC’77). Association for Computing Machinery, New York, 77-90.

[14]

Arnaud Durand and Etienne Grandjean. 2007. First-order queries on structures of bounded degree are computable with constant delay. ACM Trans. Comput. Logic 8, 4, Article 21 (Aug. 2007).

Digital Library

[15]

Friedrich Eisenbrand and Fabrizio Grandoni. 2004. On the complexity of fixed parameter clique and dominating set. Theoretical Computer Science 326, 1–3 (2004), 57–67.

Digital Library

[16]

Fernando Florenzano, Cristian Riveros, Martín Ugarte, Stijn Vansummeren, and Domagoj Vrgoc. 2018. Constant delay algorithms for regular document spanners. In Proceedings of PODS. ACM, 165–177.

Digital Library

[17]

Jörg Flum, Markus Frick, and Martin Grohe. 2002. Query evaluation via tree-decompositions. J. ACM 49, 6 (2002), 716–752.

Digital Library

[18]

Etienne Grandjean. 1996. Sorting, linear time and the satisfiability problem. Ann. Math. Artif. Intell. 16 (1996), 183–236.

[19]

Muhammad Idris, Martin Ugarte, and Stijn Vansummeren. 2017. The dynamic Yannakakis algorithm: Compact and efficient query processing under updates. In Proceedings of the 2017 ACM International Conference on Management of Data (SIGMOD’17). ACM, New York, 1259–1274.

Digital Library

[20]

Wojciech Kazana. 2013. Query evaluation with constant delay. Theses. École normale supérieure de Cachan - ENS Cachan. https://tel.archives-ouvertes.fr/tel-00919786

[21]

François Le Gall. 2014. Powers of tensors and fast matrix multiplication. In Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC’14). ACM, New York, 296–303.

Digital Library

[22]

Andrea Lincoln, Virginia Vassilevska Williams, and R. Ryan Williams. 2018. Tight hardness for shortest cycles and paths in sparse graphs. In Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018). 1236–1252.

[23]

Bernard M. E. Moret and Henry D. Shapiro. 1991. Algorithms from P to NP: Volume 1: Design & Efficiency. Benjamin-Cummings.

[24]

Matthias Niewerth and Luc Segoufin. 2018. Enumeration of MSO queries on strings with constant delay and logarithmic updates. In Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (Houston, TX, June 10-15, 2018), Jan Van den Bussche and Marcelo Arenas (Eds.). ACM, 179–191.

Digital Library

[25]

Nicole Schweikardt, Luc Segoufin, and Alexandre Vigny. 2018. Enumeration for FO queries over nowhere dense graphs. In Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (Houston, TX, June 10-15, 2018), Jan Van den Bussche and Marcelo Arenas (Eds.). ACM, 151–163.

Digital Library

[26]

Luc Segoufin. 2015. Constant delay enumeration for conjunctive queries. SIGMOD Rec. 44, 1 (May 2015), 10–17.

Digital Library

[27]

Luc Segoufin and Alexandre Vigny. 2017. Constant delay enumeration for FO queries over databases with local bounded expansion. In ICDT 2017 (Leibniz International Proceedings in Informatics (LIPIcs)), Michael Benedikt and Giorgio Orsi (Eds.), Vol. 68. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 20:1–20:16.

[28]

Yann Strozecki. 2010. Enumeration complexity and matroid decomposition. Ph.D. Dissertation. Université Paris Diderot - Paris 7.

[29]

Mihalis Yannakakis. 1981. Algorithms for acyclic database schemes. In Proceedings of the 7th International Conference on Very Large Data Bases - Volume 7 (VLDB’81). VLDB Endowment, 82–94. http://dl.acm.org/citation.cfm?id=1286831.1286840.

Digital Library

Cited By

Wang QLuo QWang Y(2024)Relational Algorithms for Top-k Query EvaluationProceedings of the ACM on Management of Data10.1145/36549712:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654971
Zhao HDeep SKoutris PRoy STannen V(2024)Evaluating Datalog over Semirings: A Grounding-based ApproachProceedings of the ACM on Management of Data10.1145/36515912:2(1-26)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651591
Zhao HFan AOuyang XKoutris P(2024)Conjunctive Queries with Negation and Aggregation: A Linear Time CharacterizationProceedings of the ACM on Management of Data10.1145/36511382:2(1-19)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651138
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Index Terms

On the Enumeration Complexity of Unions of Conjunctive Queries
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Theory and algorithms for application domains
    1. Database theory
      1. Database query languages (principles)
      2. Database query processing and optimization (theory)

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cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 46, Issue 2

Best of PODS 2019 and Regular Papers

June 2021

182 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/3468529

Editor:
Christopher Jermaine
Rice University, USA

Issue’s Table of Contents

Copyright © 2021 ACM.

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Association for Computing Machinery

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Publication History

Published: 29 May 2021

Accepted: 01 February 2021

Revised: 01 October 2020

Received: 01 March 2020

Published in TODS Volume 46, Issue 2

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Cited By

Wang QLuo QWang Y(2024)Relational Algorithms for Top-k Query EvaluationProceedings of the ACM on Management of Data10.1145/36549712:3(1-27)Online publication date: 30-May-2024
https://dl.acm.org/doi/10.1145/3654971
Zhao HDeep SKoutris PRoy STannen V(2024)Evaluating Datalog over Semirings: A Grounding-based ApproachProceedings of the ACM on Management of Data10.1145/36515912:2(1-26)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651591
Zhao HFan AOuyang XKoutris P(2024)Conjunctive Queries with Negation and Aggregation: A Linear Time CharacterizationProceedings of the ACM on Management of Data10.1145/36511382:2(1-19)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651138
Koutris PDeep S(2023)The Fine-Grained Complexity of CFL ReachabilityProceedings of the ACM on Programming Languages10.1145/35712527:POPL(1713-1739)Online publication date: 11-Jan-2023
https://dl.acm.org/doi/10.1145/3571252
Bucchi MGrez AQuintana ARiveros CVansummeren S(2022)COREProceedings of the VLDB Endowment10.14778/3538598.353861515:9(1951-1964)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.14778/3538598.3538615
Dalirrooyfard MJin CWilliams VWein N(2022)Approximation Algorithms and Hardness for n-Pairs Shortest Paths and All-Nodes Shortest Cycles2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00034(290-300)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00034

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