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The Fine Classification of Conjunctive Queries and Parameterized Logarithmic Space

Authors:

Moritz MüllerAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 7, Issue 2

Article No.: 7, Pages 1 - 27

https://doi.org/10.1145/2751316

Published: 11 May 2015 Publication History

Abstract

We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of Boolean conjunctive queries according to the complexity of this problem. Previous work showed that a set of conjunctive queries is fixed-parameter tractable precisely when the set is equivalent to a set of queries having bounded treewidth. We present a fine classification of query sets up to parameterized logarithmic space reduction. We show that, in the bounded treewidth regime, there are three complexity degrees and that the properties that determine the degree of a query set are bounded pathwidth and bounded tree depth. We also engage in a study of the two higher degrees via logarithmic space machine characterizations and complete problems. Our work yields a significantly richer perspective on the complexity of conjunctive queries and, at the same time, suggests new avenues of research in parameterized complexity.

References

[1]

S. Abiteboul, R. Hull, and V. Vianu. 1995. Foundations of Databases. Addison-Wesley.

Digital Library

[2]

A. Blumensath and B. Courcelle. 2010. On the monadic second-order transduction hierarchy. Logical Methods in Computer Science 6, 2 (2010).

[3]

H. Bodlaender. 1998. A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science 209 (1998), 1--45.

Digital Library

[4]

Ashok K. Chandra and Philip M. Merlin. 1977. Optimal implementation of conjunctive queries in relational data bases. In Proceedings of STOC’77. 77--90.

Digital Library

[5]

Hubie Chen and Martin Grohe. 2010. Constraint satisfaction with succinctly specified relations. Journal of Computing System Science 76, 8 (2010), 847--860.

Digital Library

[6]

Y. Chen, J. Flum, and M. Grohe. 2003. Bounded nondeterminism and alternation in parameterized complexity theory. In Proceedings of the 18th IEEE Conference on Computational Complexity. 13--29.

[7]

Y. Chen and M. Müller. 2014. Bounded variable logic, parameterized logarithmic space and Savitch’s theorem. 39th Mathematical Foundations of Computer Science (2014).

[8]

A. Chiu, G. Davida, and B. Litow. 2001. Division in logspace-uniform NC¹. Theoretical Informatics and Applications 35 (2001), 259--275.

[9]

N. Creignou, S. Khanna, and M. Sudan. 2001. Complexity Classification of Boolean Constraint Satisfaction Problems. Society for Industrial and Applied Mathematics.

Digital Library

[10]

Nadia Creignou, Phokion G. Kolaitis, and Heribert Vollmer (Eds.). 2008. Complexity of Constraints - An Overview of Current Research Themes. Lecture Notes in Computer Science, Vol. 5250. Springer.

Digital Library

[11]

V. Dalmau and P. Jonsson. 2004. The complexity of counting homomorphisms seen from the other side. Theoretical Computer Science 329 (2004), 315--323.

Digital Library

[12]

R. G. Downey and M. R. Fellows. 1999. Parameterized Complexity. Springer.

Digital Library

[13]

M. Elberfeld, C. Stockhusen, and T. Tantau. 2012. On the space complexity of parameterized problems. 7th International Symposium of Parameterized and Exact Computation, Springer LNCS 7535 (2012), 206--217.

Digital Library

[14]

T. Feder and M. Y. Vardi. 1999. The computational structure of monotone monadic SNP and constraint satisfaction: A study through datalog and group theory. SIAM Journal on Computing 28, 1 (1999), 57--104.

Digital Library

[15]

J. Flum, M. Frick, and M. Grohe. 2002. Query evaluation via tree-decompositions. Journal of the ACM 49, 6 (2002), 716--752.

Digital Library

[16]

J. Flum and M. Grohe. 2003. Describing parameterized complexity classes. Information and Computation 187 (2003), 291--319.

Digital Library

[17]

J. Flum and M. Grohe. 2006a. The parameterized complexity of counting problems. SIAM Journal on Computing 33 (2006), 892--922.

Digital Library

[18]

J. Flum and M. Grohe. 2006b. Parameterized Complexity Theory. Springer.

Digital Library

[19]

Georg Gottlob, Nicola Leone, and Francesco Scarcello. 2001. The complexity of acyclic conjunctive queries. Journal of the ACM 48, 3 (2001), 431--498.

Digital Library

[20]

Georg Gottlob, Nicola Leone, and Francesco Scarcello. 2002. Hypertree decompositions and tractable queries. Journal of Computer and Systems Science. 64, 3 (2002), 579--627.

Digital Library

[21]

Martin Grohe. 2007. The complexity of homomorphism and constraint satisfaction problems seen from the other side. Journal of the ACM 54, 1 (2007).

Digital Library

[22]

Martin Grohe, Thomas Schwentick, and Luc Segoufin. 2001. When is the evaluation of conjunctive queries tractable&quest; In STOC 2001.

Digital Library

[23]

P. Kolaitis and M. Y. Vardi. 1998. Conjunctive-query containment and constraint satisfaction. In Proceedings of the 17th ACM Symposium on Principles of Database Systems 10 (1998, full version at: http://www.cs.rice.edu/&sim;vardi/papers), 205--213.

Digital Library

[24]

R. E. Ladner and N. A. Lynch. 1976. Relativization of questions about log space computability. Mathematical Systems Theory 10 (1976), 19--32.

[25]

Dániel Marx. 2010a. Can you beat treewidth&quest; Theory of Computing 6, 1 (2010), 85--112. hlink="http://dx.doi.org/10.4086/toc.2010.v006a005" &quest;http://dx.&quest;brk&quest;doi.org/10.4086/toc.2010.v006a005

[26]

Dániel Marx. 2010b. Tractable hypergraph properties for constraint satisfaction and conjunctive queries. In Proceedings of the 42nd ACM Symposium on Theory of Computing. 735--744.

Digital Library

[27]

J. Nešetřil and P. O. de Mendez. 2006. Tree depth, subgraph coloring, and homomorphism bounds. European Journal of Combinatorics 27, 6 (2006), 1022--1041.

Digital Library

[28]

C. Papadimitriou and M. Yannakakis. 1999. On the complexity of database queries. Journal of Computers System Science 58, 3 (1999), 407--427.

Digital Library

[29]

Nicole Schweikardt, Thomas Schwentick, and Luc Segoufin. 2009. Database theory: Query languages. In Algorithms and Theory of Computation Handbook (2nd ed.), Mikhail J. Atallah and Marina Blanton (Eds.). Vol. 2: Special Topics and Techniques. CRC Press, Chapter 19.

Digital Library

Cited By

Haak AMeier APrakash ORao B(2023)Parameterised Counting in LogspaceAlgorithmica10.1007/s00453-023-01114-285:10(2923-2961)Online publication date: 21-Apr-2023
https://dl.acm.org/doi/10.1007/s00453-023-01114-2
Bannach MTantau T(2021)On the Descriptive Complexity of Color CodingAlgorithms10.3390/a1403009614:3(96)Online publication date: 19-Mar-2021
https://doi.org/10.3390/a14030096
Mahmood YMeier A(2021)Parameterised complexity of model checking and satisfiability in propositional dependence logicAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09730-wOnline publication date: 27-Feb-2021
https://doi.org/10.1007/s10472-021-09730-w
Show More Cited By

Index Terms

The Fine Classification of Conjunctive Queries and Parameterized Logarithmic Space
1. Information systems
  1. Data management systems
    1. Query languages
2. Theory of computation
  1. Logic

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cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 7, Issue 2

May 2015

101 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/2775140

Editor:
Eric Allender
Rutgers University, USA

Issue’s Table of Contents

Copyright © 2015 ACM.

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Association for Computing Machinery

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Publication History

Published: 11 May 2015

Accepted: 01 June 2014

Revised: 01 April 2014

Received: 01 May 2013

Published in TOCT Volume 7, Issue 2

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Cited By

Haak AMeier APrakash ORao B(2023)Parameterised Counting in LogspaceAlgorithmica10.1007/s00453-023-01114-285:10(2923-2961)Online publication date: 21-Apr-2023
https://dl.acm.org/doi/10.1007/s00453-023-01114-2
Bannach MTantau T(2021)On the Descriptive Complexity of Color CodingAlgorithms10.3390/a1403009614:3(96)Online publication date: 19-Mar-2021
https://doi.org/10.3390/a14030096
Mahmood YMeier A(2021)Parameterised complexity of model checking and satisfiability in propositional dependence logicAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09730-wOnline publication date: 27-Feb-2021
https://doi.org/10.1007/s10472-021-09730-w
Mahmood YMeier A(2020)Parameterised Complexity of Model Checking and Satisfiability in Propositional Dependence LogicFoundations of Information and Knowledge Systems10.1007/978-3-030-39951-1_10(157-174)Online publication date: 17-Feb-2020
https://dl.acm.org/doi/10.1007/978-3-030-39951-1_10
Chen HSuciu DSkritek SKoch C(2019)The Selfish Models PropertyProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319682(383-398)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319682
Chen HYoshida YSuciu DSkritek SKoch C(2019)Testability of Homomorphism InadmissibilityProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319679(365-382)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319679
Chen YFlum J(2018)Tree-depth, quantifier elimination, and quantifier rankProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3209108.3209160(225-234)Online publication date: 9-Jul-2018
https://dl.acm.org/doi/10.1145/3209108.3209160
Chen HMüller M(2017)One Hierarchy Spawns AnotherACM Transactions on Computational Logic10.1145/314380518:4(1-37)Online publication date: 3-Nov-2017
https://dl.acm.org/doi/10.1145/3143805
Chen H(2017)The Tractability Frontier of Graph-Like First-Order Query SetsJournal of the ACM10.1145/307340964:4(1-29)Online publication date: 17-Aug-2017
https://dl.acm.org/doi/10.1145/3073409
Chen HMüller M(2017)The Parameterized Space Complexity of Embedding Along a PathTheory of Computing Systems10.1007/s00224-016-9728-761:3(851-870)Online publication date: 1-Oct-2017
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