research-article

Minimization of Tree Patterns

Authors:

Wojciech CzerwiŃski,

Matthias Niewerth,

Paweł ParysAuthors Info & Claims

Journal of the ACM (JACM), Volume 65, Issue 4

Article No.: 26, Pages 1 - 46

https://doi.org/10.1145/3180281

Published: 25 July 2018 Publication History

Abstract

Many of today’s graph query languages are based on graph pattern matching. We investigate optimization of tree-shaped patterns that have transitive closure operators. Such patterns not only appear in the context of graph databases but also were originally studied for querying tree-structured data, where they can perform child, descendant, node label, and wildcard tests.

The minimization problem aims at reducing the number of nodes in patterns and goes back to the early 2000s. We provide an example showing that, in contrast to earlier claims, tree patterns cannot be minimized by deleting nodes only. The example resolves the M =^? NR problem, which asks if a tree pattern is minimal if and only if it is nonredundant. The example can be adapted to prove that minimization is Σ^P₂-complete, which resolves another question that was open since the early research on the problem. The latter result shows that, unless NP = Π^P₂, more general approaches for minimizing tree patterns are also bound to fail in general.

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Cited By

Martens WLibkin LBarceló P(2022)Towards Theory for Real-World DataProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3526066(261-276)Online publication date: 12-Jun-2022
https://dl.acm.org/doi/10.1145/3517804.3526066
Schmid M(2022)Conjunctive Regular Path Queries with Capture GroupsACM Transactions on Database Systems10.1145/351423047:2(1-52)Online publication date: 23-May-2022
https://dl.acm.org/doi/10.1145/3514230
Dutta PSaxena NSinhababu A(2022)Discovering the Roots: Uniform Closure Results for Algebraic Classes Under FactoringJournal of the ACM10.1145/351035969:3(1-39)Online publication date: 11-Jun-2022
https://dl.acm.org/doi/10.1145/3510359
Show More Cited By

Index Terms

Minimization of Tree Patterns
1. Information systems
  1. Data management systems
    1. Query languages
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 65, Issue 4

Distributed Computing, Cryptography, Distributed Computing, Cryptography, Coding Theory, Automata Theory, Complexity Theory, Programming Languages, Algorithms, Invited Paper Foreword and Databases

August 2018

307 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3208081

Editor:
Éva Tardos
Cornell University

Issue’s Table of Contents

Copyright © 2018 ACM.

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].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 July 2018

Accepted: 01 January 2018

Revised: 01 October 2017

Received: 01 January 2017

Published in JACM Volume 65, Issue 4

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Cited By

Martens WLibkin LBarceló P(2022)Towards Theory for Real-World DataProceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3517804.3526066(261-276)Online publication date: 12-Jun-2022
https://dl.acm.org/doi/10.1145/3517804.3526066
Schmid M(2022)Conjunctive Regular Path Queries with Capture GroupsACM Transactions on Database Systems10.1145/351423047:2(1-52)Online publication date: 23-May-2022
https://dl.acm.org/doi/10.1145/3514230
Dutta PSaxena NSinhababu A(2022)Discovering the Roots: Uniform Closure Results for Algebraic Classes Under FactoringJournal of the ACM10.1145/351035969:3(1-39)Online publication date: 11-Jun-2022
https://dl.acm.org/doi/10.1145/3510359
Soloviev MHalpern J(2022)Information Acquisition Under Resource Limitations in a Noisy EnvironmentJournal of the ACM10.1145/351002469:3(1-37)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1145/3510024
Li YChen HChen Z(2022)Learning Disjunctive Multiplicity Expressions and Disjunctive Generalize Multiplicity Expressions From Both Positive and Negative ExamplesThe Computer Journal10.1093/comjnl/bxac03766:7(1733-1748)Online publication date: 18-Apr-2022
https://doi.org/10.1093/comjnl/bxac037
Schmid MSuciu DTao YWei Z(2020)Conjunctive Regular Path Queries with String VariablesProceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3375395.3387663(361-374)Online publication date: 14-Jun-2020
https://dl.acm.org/doi/10.1145/3375395.3387663
Bourhis PReutter JVrgoč D(2020)JSONInformation Systems10.1016/j.is.2019.10147889:COnline publication date: 1-Mar-2020
https://dl.acm.org/doi/10.1016/j.is.2019.101478
Bonifati AMartens WTimm T(2019)An analytical study of large SPARQL query logsThe VLDB Journal10.1007/s00778-019-00558-929:2-3(655-679)Online publication date: 2-Aug-2019
https://doi.org/10.1007/s00778-019-00558-9

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