research-article

Structural tractability of counting of solutions to conjunctive queries

Authors:

Stefan MengelAuthors Info & Claims

ICDT '13: Proceedings of the 16th International Conference on Database Theory

Pages 81 - 92

https://doi.org/10.1145/2448496.2448508

Published: 18 March 2013 Publication History

Abstract

In this paper we explore the problem of counting solutions to conjunctive queries. We consider a parameter called the quantified star size of a formula φ which measures how the free variables are spread in φ. We show that for conjunctive queries that admit nice decomposition properties (such as being of bounded treewidth or generalized hypertree width) bounded quantified star size exactly characterizes the classes of queries for which counting the number of solutions is tractable. This also allows us to fully characterize the conjunctive queries for which counting the solutions is tractable in the case of bounded arity. To illustrate the applicability of our results, we also show that computing the quantified star size of a formula is possible in time n^O(k) for queries of generalized hypertree width k. Furthermore, quantified star size is even fixed parameter tractable parameterized by some other width measures, while it is W[1]-hard for generalized hypertree width and thus unlikely to be fixed parameter tractable. We finally show how to compute an approximation of quantified star size in polynomial time where the approximation ratio depends on the width of the input.

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Cited By

Focke JGoldberg LRoth MZivný S(2024)Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-ComplexityProceedings of the ACM on Management of Data10.1145/36516142:2(1-17)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651614
Fichte JHecher MMorak MThier PWoltran S(2023)Solving Projected Model Counting by Utilizing Treewidth and its LimitsArtificial Intelligence10.1016/j.artint.2022.103810314:COnline publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1016/j.artint.2022.103810
Grohe MSchweikardt NVan den Bussche JArenas M(2018)First-Order Query Evaluation with Cardinality ConditionsProceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196970(253-266)Online publication date: 27-May-2018
https://dl.acm.org/doi/10.1145/3196959.3196970
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Structural tractability of counting of solutions to conjunctive queries

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cover image ACM Other conferences

ICDT '13: Proceedings of the 16th International Conference on Database Theory

March 2013

301 pages

ISBN:9781450315982

DOI:10.1145/2448496

Editors:
Wang-Chiew Tan
UC Santa Cruz
,
Giovanna Guerrini
Universita' di Genova, Italy
,
Barbara Catania
Universita' di Genova, Italy
,
Anastasios Gounaris
Aristotle University of Thessaloniki, Greece

Copyright © 2013 ACM.

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Published: 18 March 2013

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EDBT/ICDT '13

EDBT/ICDT '13: Joint 2013 EDBT/ICDT Conferences

March 18 - 22, 2013

Genoa, Italy

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Cited By

Focke JGoldberg LRoth MZivný S(2024)Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-ComplexityProceedings of the ACM on Management of Data10.1145/36516142:2(1-17)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3651614
Fichte JHecher MMorak MThier PWoltran S(2023)Solving Projected Model Counting by Utilizing Treewidth and its LimitsArtificial Intelligence10.1016/j.artint.2022.103810314:COnline publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1016/j.artint.2022.103810
Grohe MSchweikardt NVan den Bussche JArenas M(2018)First-Order Query Evaluation with Cardinality ConditionsProceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196970(253-266)Online publication date: 27-May-2018
https://dl.acm.org/doi/10.1145/3196959.3196970
Chen HMengel SAceto LIngólfsdóttir A(2017)The logic of counting query answersProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330020(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330020
Khamis MNgo HRudra A(2017)Juggling Functions Inside a DatabaseACM SIGMOD Record10.1145/3093754.309375746:1(6-13)Online publication date: 12-May-2017
https://dl.acm.org/doi/10.1145/3093754.3093757
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 HMengel S(2017)The logic of counting query answers2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2017.8005085(1-12)Online publication date: Jun-2017
https://doi.org/10.1109/LICS.2017.8005085
Abo Khamis MNgo HRudra AMilo TTan W(2016)FAQProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902280(13-28)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1145/2902251.2902280
Segoufin L(2015)Constant Delay Enumeration for Conjunctive QueriesACM SIGMOD Record10.1145/2783888.278389444:1(10-17)Online publication date: 21-May-2015
https://dl.acm.org/doi/10.1145/2783888.2783894
Chen HHenzinger TMiller D(2014)The tractability frontier of graph-like first-order query setsProceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1145/2603088.2603119(1-9)Online publication date: 14-Jul-2014
https://dl.acm.org/doi/10.1145/2603088.2603119
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