Uniform Reliability of Self-Join-Free Conjunctive Queries

Authors Antoine Amarilli , Benny Kimelfeld



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Antoine Amarilli
  • LTCI, Télécom Paris, Institut Polytechnique de Paris, France
Benny Kimelfeld
  • Technion - Israel Institute of Technology, Haifa, Israel

Acknowledgements

The authors are very grateful to Kuldeep S. Meel and Dan Suciu for insightful discussions on the topic of this paper.

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Antoine Amarilli and Benny Kimelfeld. Uniform Reliability of Self-Join-Free Conjunctive Queries. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICDT.2021.17

Abstract

The reliability of a Boolean Conjunctive Query (CQ) over a tuple-independent probabilistic database is the probability that the CQ is satisfied when the tuples of the database are sampled one by one, independently, with their associated probability. For queries without self-joins (repeated relation symbols), the data complexity of this problem is fully characterized in a known dichotomy: reliability can be computed in polynomial time for hierarchical queries, and is #P-hard for non-hierarchical queries. Hierarchical queries also characterize the tractability of queries for other tasks: having read-once lineage formulas, supporting insertion/deletion updates to the database in constant time, and having a tractable computation of tuples' Shapley and Banzhaf values. In this work, we investigate a fundamental counting problem for CQs without self-joins: how many sets of facts from the input database satisfy the query? This is equivalent to the uniform case of the query reliability problem, where the probability of every tuple is required to be 1/2. Of course, for hierarchical queries, uniform reliability is in polynomial time, like the reliability problem. However, it is an open question whether being hierarchical is necessary for the uniform reliability problem to be in polynomial time. In fact, the complexity of the problem has been unknown even for the simplest non-hierarchical CQs without self-joins. We solve this open question by showing that uniform reliability is #P-complete for every non-hierarchical CQ without self-joins. Hence, we establish that being hierarchical also characterizes the tractability of unweighted counting of the satisfying tuple subsets. We also consider the generalization to query reliability where all tuples of the same relation have the same probability, and give preliminary results on the complexity of this problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database query processing and optimization (theory)
Keywords
  • Hierarchical conjunctive queries
  • query reliability
  • tuple-independent database
  • counting problems
  • #P-hardness

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References

  1. Antoine Amarilli and Benny Kimelfeld. https://arxiv.org/abs/1908.07093. In https://databasetheory.org/node/106, 2021.
  2. Paul Beame, Guy Van den Broeck, Eric Gribkoff, and Dan Suciu. https://arxiv.org/abs/1412.1505. In PODS, pages 313-328. ACM, 2015.
  3. Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. https://arxiv.org/abs/1702.06370. In PODS, pages 303-318. ACM, 2017.
  4. Andrei A. Bulatov. https://www.cs.sfu.ca/~abulatov/papers/counting-acm.pdf. J. ACM, 60(5):34:1-34:41, 2013.
  5. Supratik Chakraborty, Dror Fried, Kuldeep S Meel, and Moshe Y Vardi. https://www.ijcai.org/Proceedings/15/Papers/103.pdf. In IJCAI, 2015.
  6. Nilesh Dalvi and Dan Suciu. https://homes.cs.washington.edu/~suciu/vldbj-probdb.pdf. VLDB Journal, 16(4):523-544, 2007.
  7. Nilesh Dalvi and Dan Suciu. https://homes.cs.washington.edu/~suciu/jacm-dichotomy.pdf. J. ACM, 59(6), 2012.
  8. Nilesh N. Dalvi, Christopher Ré, and Dan Suciu. https://homes.cs.washington.edu/~suciu/file15_cacm-paper.pdf. Commun. ACM, 52(7):86-94, 2009.
  9. Pradeep Dubey and Lloyd S. Shapley. Mathematical properties of the Banzhaf power index. Mathematics of Operations Research, 4(2):99-131, 1979. Google Scholar
  10. Erich Grädel, Yuri Gurevich, and Colin Hirsch. https://www.researchgate.net/profile/Yuri_Gurevich2/publication/2900852_The_Complexity_of_Query_Reliability/links/0c96053321102376cd000000/The-Complexity-of-Query-Reliability.pdf. In PODS, pages 227-234. ACM Press, 1998.
  11. Eric Gribkoff and Dan Suciu. http://www.vldb.org/pvldb/vol9/p552-gribkoff.pdf. PVLDB, 9(7):552-563, 2016.
  12. B. Grofman and H. Scarrow. Iannucci and Its Aftermath: The Application of the Banzhaf Index to Weighted Voting in the State of New York, pages 168-183. Physica-Verlag HD, Heidelberg, 1979. URL: https://doi.org/10.1007/978-3-662-41501-6_10.
  13. Abhay Kumar Jha and Dan Suciu. http://vldb.org/pvldb/vol5/p1160_abhayjha_vldb2012.pdf. PVLDB, 5(11):1160-1171, 2012.
  14. Batya Kenig and Dan Suciu. https://arxiv.org/abs/2008.00896. CoRR, abs/2008.00896, 2020.
  15. Ester Livshits, Leopoldo E. Bertossi, Benny Kimelfeld, and Moshe Sebag. https://drops.dagstuhl.de/opus/volltexte/2020/11944/. In ICDT, volume 155 of LIPIcs, pages 20:1-20:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.
  16. Dany Maslowski and Jef Wijsen. https://www.sciencedirect.com/science/article/pii/S0022000013000214. J. Comput. Syst. Sci., 79(6):958-983, 2013.
  17. Dany Maslowski and Jef Wijsen. http://www.openproceedings.org/ICDT/2014/paper_17.pdf. In ICDT, pages 155-164. OpenProceedings.org, 2014.
  18. Dan Olteanu and Jiewen Huang. https://www.cs.ox.ac.uk/people/dan.olteanu/papers/oh-sum08.pdf. In SUM, volume 5291 of Lecture Notes in Computer Science, pages 326-340. Springer, 2008.
  19. J. Scott Provan and Michael O. Ball. The complexity of counting cuts and of computing the probability that a graph is connected. SIAM Journal on Computing, 12(4), 1983. Google Scholar
  20. Alvin E Roth. The Shapley value: Essays in honor of Lloyd S. Shapley. Cambridge University Press, 1988. Google Scholar
  21. Babak Salimi, Leopoldo E. Bertossi, Dan Suciu, and Guy Van den Broeck. https://arxiv.org/abs/1603.02705. In TAPP, 2016.
  22. L.S. Shapley. https://www.pnas.org/content/39/10/1095. Proceedings of the National Academy of Sciences of the United States of America, 39:1095-1100, 1953.
  23. Dan Suciu, Dan Olteanu, Christopher Ré, and Christoph Koch. Probabilistic Databases. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, 2011. Google Scholar
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