research-article

Tractable Orders for Direct Access to Ranked Answers of Conjunctive Queries

Authors:

Nikolaos Tziavelis,

Wolfgang Gatterbauer,

Benny Kimelfeld,

Mirek RiedewaldAuthors Info & Claims

ACM Transactions on Database Systems, Volume 48, Issue 1

Article No.: 1, Pages 1 - 45

https://doi.org/10.1145/3578517

Published: 13 March 2023 Publication History

Abstract

We study the question of when we can provide direct access to the k-th answer to a Conjunctive Query (CQ) according to a specified order over the answers in time logarithmic in the size of the database, following a preprocessing step that constructs a data structure in time quasilinear in database size. Specifically, we embark on the challenge of identifying the tractable answer orderings, that is, those orders that allow for such complexity guarantees. To better understand the computational challenge at hand, we also investigate the more modest task of providing access to only a single answer (i.e., finding the answer at a given position), a task that we refer to as the selection problem, and ask when it can be performed in quasilinear time. We also explore the question of when selection is indeed easier than ranked direct access.

We begin with lexicographic orders. For each of the two problems, we give a decidable characterization (under conventional complexity assumptions) of the class of tractable lexicographic orders for every CQ without self-joins. We then continue to the more general orders by the sum of attribute weights and establish the corresponding decidable characterizations, for each of the two problems, of the tractable CQs without self-joins. Finally, we explore the question of when the satisfaction of Functional Dependencies (FDs) can be utilized for tractability and establish the corresponding generalizations of our characterizations for every set of unary FDs.

References

[1]

Amir Abboud and Virginia Vassilevska Williams. 2014. Popular conjectures imply strong lower bounds for dynamic problems. In FOCS. 434–443. DOI:

Digital Library

[2]

Nir Ailon and Bernard Chazelle. 2005. Lower bounds for linear degeneracy testing. J. ACM 52, 2 (2005), 157–171. DOI:

Digital Library

[3]

Noga Alon, Raphael Yuster, and Uri Zwick. 1997. Finding and counting given length cycles. Algorithmica 17, 3 (1997), 209–223. DOI:

[4]

Guillaume Bagan, Arnaud Durand, and Etienne Grandjean. 2007. On acyclic conjunctive queries and constant delay enumeration. In CSL. 208–222. DOI:

[5]

Guillaume Bagan, Arnaud Durand, Etienne Grandjean, and Frédéric Olive. 2008. Computing the jth solution of a first-order query. RAIRO-Theoret. Inform. Applic. 42, 1 (2008), 147–164. DOI:

[6]

Ilya Baran, Erik D. Demaine, and Mihai Pǎtraşcu. 2005. Subquadratic algorithms for 3SUM. In Algorithms and Data Structures. 409–421. DOI:

Digital Library

[7]

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

Digital Library

[8]

Christoph Berkholz, Jens Keppeler, and Nicole Schweikardt. 2017. Answering conjunctive queries under updates. In PODS. 303–318. DOI:

Digital Library

[9]

Manuel Blum, Robert W. Floyd, Vaughan Pratt, Ronald L. Rivest, and Robert E. Tarjan. 1973. Time bounds for selection. J. Comput. Syst. Sci. 7, 4 (1973), 448–461. DOI:

Digital Library

[10]

Pierre Bourhis, Alejandro Grez, Louis Jachiet, and Cristian Riveros. 2021. Ranked enumeration of MSO logic on words. In ICDT. 20:1–20:19. DOI:

[11]

Johann Brault-Baron. 2013. De la Pertinence de l’énumération: Complexité en Logiques Propositionnelle et du Premier Ordre. Ph.D. Dissertation. U. de Caen. Retrieved from: https://hal.archives-ouvertes.fr/tel-01081392.

[12]

Nofar Carmeli and Markus Kröll. 2020. Enumeration complexity of conjunctive queries with functional dependencies. Theor. Comput. Syst. 64, 5 (2020), 828–860. DOI:

[13]

Nofar Carmeli, Nikolaos Tziavelis, Wolfgang Gatterbauer, Benny Kimelfeld, and Mirek Riedewald. 2021. Tractable orders for direct access to ranked answers of conjunctive queries. In PODS. 325–341. DOI:

Digital Library

[14]

Nofar Carmeli, Shai Zeevi, Christoph Berkholz, Benny Kimelfeld, and Nicole Schweikardt. 2020. Answering (unions of) conjunctive queries using random access and random-order enumeration. In PODS. 393–409. DOI:

Digital Library

[15]

Shaleen Deep and Paraschos Koutris. 2021. Ranked enumeration of conjunctive query results. In ICDT. 5:1–5:19. DOI:

[16]

Arnaud Durand. 2020. Fine-grained complexity analysis of queries: From decision to counting and enumeration. In PODS. 331–346. DOI:

Digital Library

[17]

Jeff Erickson. 1995. Lower bounds for linear satisfiability problems. In SODA. 388–395.

Digital Library

[18]

Robert W. Floyd and Ronald L. Rivest. 1975. Expected time bounds for selection. Commun. ACM 18, 3 (1975), 165–172. DOI:

Digital Library

[19]

Greg N. Frederickson. 1993. An optimal algorithm for selection in a min-heap. Inf. Comput. 104, 2 (1993), 197–214. DOI:

Digital Library

[20]

Greg N. Frederickson and Donald B. Johnson. 1984. Generalized selection and ranking: Sorted matrices. SIAM J. Comput. 13, 1 (1984), 14–30. DOI:

[21]

Cibele Freire, Wolfgang Gatterbauer, Neil Immerman, and Alexandra Meliou. 2015. The complexity of resilience and responsibility for self-join-free conjunctive queries. Proc. VLDB Endow. 9, 3 (2015), 180–191. DOI:

Digital Library

[22]

Anka Gajentaan and Mark H. Overmars. 1995. On a class of O(n2) problems in computational geometry. Computat. Geom. 5, 3 (1995), 165–185. DOI:

Digital Library

[23]

Wolfgang Gatterbauer and Dan Suciu. 2015. Approximate lifted inference with probabilistic databases. Proc. VLDB Endow. 8, 5 (2015), 629–640. DOI:

Digital Library

[24]

Wolfgang Gatterbauer and Dan Suciu. 2017. Dissociation and propagation for approximate lifted inference with standard relational database management systems. VLDB J. 26, 1 (2017), 5–30. DOI:

Digital Library

[25]

Martin Charles Golumbic. 1980. Algorithmic Graph Theory and Perfect Graphs. Elsevier, 81–104. DOI:

[26]

Georg Gottlob, Gianluigi Greco, Nicola Leone, and Francesco Scarcello. 2016. Hypertree decompositions: Questions and answers. In PODS. 57–74. DOI:

Digital Library

[27]

Etienne Grandjean. 1996. Sorting, linear time and the satisfiability problem. Ann. Math. Artif. Intell. 16, 1 (1996), 183–236. DOI:

[28]

Egbert Harzheim. 2006. Ordered Sets. Vol. 7. Springer Science & Business Media. DOI:

[29]

Russell Impagliazzo and Ramamohan Paturi. 2001. On the complexity of K-SAT. J. Comput. Syst. Sci. 62, 2 (2001), 367–375. DOI:

Digital Library

[30]

Donald B. Johnson and Tetsuo Mizoguchi. 1978. Selecting the Kth element in \(X + Y\) and \(X_1 + X_2 + \cdots + X_m\). SIAM J. Comput. 7, 2 (1978), 147–153. DOI:

Digital Library

[31]

Jens Keppeler. 2020. Answering Conjunctive Queries and FO+MOD Queries under Updates. Ph.D. Dissertation. Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät. DOI:

[32]

Benny Kimelfeld. 2012. A dichotomy in the complexity of deletion propagation with functional dependencies. In PODS. 191–202. DOI:

Digital Library

[33]

Andrea Lincoln, Virginia Vassilevska Williams, and R. Ryan Williams. 2018. Tight hardness for shortest cycles and paths in sparse graphs. In SODA. 1236–1252. DOI:

[34]

Stefan Mengel. 2021. A short note on the counting complexity of conjunctive queries. CoRR abs/2112.01108 (2021).

[35]

A. Mirzaian and E. Arjomandi. 1985. Selection in X + Y and matrices with sorted rows and columns. Inf. Process. Lett. 20, 1 (1985), 13–17. DOI:

[36]

Dan Olteanu and Maximilian Schleich. 2016. Factorized databases. SIGMOD Rec. 45, 2 (2016), 5–16. DOI:

Digital Library

[37]

Dan Olteanu and Jakub Zavodny. 2012. Factorised representations of query results: Size bounds and readability. In ICDT. 285–298. DOI:

Digital Library

[38]

Mihai Patrascu. 2010. Towards polynomial lower bounds for dynamic problems. In STOC. 603. DOI:

Digital Library

[39]

Mihai Pătraşcu and Ryan Williams. 2010. On the possibility of faster SAT algorithms. In SODA. 1065–1075. DOI:

[40]

Nikolaos Tziavelis, Deepak Ajwani, Wolfgang Gatterbauer, Mirek Riedewald, and Xiaofeng Yang. 2020. Optimal algorithms for ranked enumeration of answers to full conjunctive queries. Proc. VLDB Endow. 13, 9 (2020), 1582–1597. DOI:

Digital Library

[41]

Nikolaos Tziavelis, Wolfgang Gatterbauer, and Mirek Riedewald. 2020. Optimal join algorithms meet top-k. In SIGMOD. 2659–2665. DOI:

Digital Library

[42]

Nikolaos Tziavelis, Wolfgang Gatterbauer, and Mirek Riedewald. 2021. Beyond equi-joins: Ranking, enumeration and factorization. Proc. VLDB Endow. 14, 11 (2021), 2599–2612. DOI:

Digital Library

[43]

Nikolaos Tziavelis, Wolfgang Gatterbauer, and Mirek Riedewald. 2022. Any-k algorithms for enumerating ranked answers to conjunctive queries. CoRR abs/2205.05649 (2022).

[44]

Virginia Vassilevska Williams. 2015. Hardness of easy problems: Basing hardness on popular conjectures such as the strong exponential time hypothesis (invited talk). In IPEC. 17–29. DOI:

[45]

Xiaofeng Yang, Mirek Riedewald, Rundong Li, and Wolfgang Gatterbauer. 2018. Any-\(k\) algorithms for exploratory analysis with conjunctive queries. In ExploreDB. 1–3. DOI:

Digital Library

[46]

Mihalis Yannakakis. 1981. Algorithms for acyclic database schemes. In VLDB. 82–94. Retrieved from:.

Digital Library

[47]

Zhuoyue Zhao, Robert Christensen, Feifei Li, Xiao Hu, and Ke Yi. 2018. Random sampling over joins revisited. In SIGMOD. 1525–1539. DOI:

Digital Library

Cited By

Arenas MMerkl TPichler RRiveros C(2024)Towards Tractability of the Diversity of Query Answers: Ultrametrics to the RescueProceedings of the ACM on Management of Data10.1145/36958332:5(1-26)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695833
Esmailpour ASintos S(2024)Improved Approximation Algorithms for Relational ClusteringProceedings of the ACM on Management of Data10.1145/36958312:5(1-27)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695831
Tian RZhang WWang FZhou JAlhudhaif AAlenezi F(2023)Cardinality estimation of activity trajectory similarity queries using deep learningInformation Sciences10.1016/j.ins.2023.119398646(119398)Online publication date: Oct-2023
https://doi.org/10.1016/j.ins.2023.119398

Index Terms

Tractable Orders for Direct Access to Ranked Answers 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)

Recommendations

Tractable Orders for Direct Access to Ranked Answers of Conjunctive Queries
PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

We study the question of when we can provide logarithmic-time direct access to the k-th answer to a Conjunctive Query (CQ) with a specified ordering over the answers, following a preprocessing step that constructs a data structure in time quasilinear in ...
Equivalence and minimization of conjunctive queries under combined semantics
ICDT '12: Proceedings of the 15th International Conference on Database Theory

The problems of query containment, equivalence, and minimization are fundamental problems in the context of query processing and optimization. In their classic work [2] published in 1977, Chandra and Merlin solved the three problems for the language of ...
Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-Complexity
PODS

We study the problem of counting answers to unions of conjunctive queries (UCQs) under structural restrictions on the input query. Concretely, given a class C of UCQs, the problem #UCQ (C) provides as input a UCQ Ψ ∈ C and a database D and the problem is ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 48, Issue 1

March 2023

112 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/3585397

Editor:
Christopher Jermaine
Rice University, USA

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 March 2023

Online AM: 02 January 2023

Accepted: 14 November 2022

Revised: 07 December 2021

Received: 07 December 2021

Published in TODS Volume 48, Issue 1

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

Google PhD Fellowships
German Research Foundation (DFG) Project
National Science Foundation (NSF)
French government under management of Agence Nationale de la Recherche as part of the “Investissements d’avenir” program

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
667
Total Downloads

Downloads (Last 12 months)231
Downloads (Last 6 weeks)19

Reflects downloads up to 05 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Arenas MMerkl TPichler RRiveros C(2024)Towards Tractability of the Diversity of Query Answers: Ultrametrics to the RescueProceedings of the ACM on Management of Data10.1145/36958332:5(1-26)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695833
Esmailpour ASintos S(2024)Improved Approximation Algorithms for Relational ClusteringProceedings of the ACM on Management of Data10.1145/36958312:5(1-27)Online publication date: 7-Nov-2024
https://dl.acm.org/doi/10.1145/3695831
Tian RZhang WWang FZhou JAlhudhaif AAlenezi F(2023)Cardinality estimation of activity trajectory similarity queries using deep learningInformation Sciences10.1016/j.ins.2023.119398646(119398)Online publication date: Oct-2023
https://doi.org/10.1016/j.ins.2023.119398

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Full Text

View this article in Full Text.

HTML Format

View this article in HTML Format.

Figures

Tables

Media

View full text|Download PDF

View Issue’s Table of Contents