research-article

Pattern Matching with Variables: Efficient Algorithms and Complexity Results

Authors:

Henning Fernau,

Robert Mercaş,

Markus L. SchmidAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 12, Issue 1

Article No.: 6, Pages 1 - 37

https://doi.org/10.1145/3369935

Published: 11 February 2020 Publication History

Abstract

A pattern ɑ (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of ɑ by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern matches a given word, is generally NP-complete, but can be solved in polynomial-time for restricted classes of patterns. We present efficient algorithms for the matching problem with respect to patterns with a bounded number of repeated variables and patterns with a structural restriction on the order of variables. Furthermore, we show that it is NP-complete to decide, for a given number k and a word w, whether w can be factorised into k distinct factors. As an immediate consequence of this hardness result, the injective version (i.e., different variables are replaced by different words) of the matching problem is NP-complete even for very restricted classes of patterns.

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Cited By

Fleischmann PKim SKoß TManea FNowotka DSiemer SWiedenhöft M(2023)Matching Patterns with Variables Under Simon’s CongruenceReachability Problems10.1007/978-3-031-45286-4_12(155-170)Online publication date: 5-Oct-2023
https://doi.org/10.1007/978-3-031-45286-4_12
Wu YJian BLi YJiang HWu X(2022)NetNDP: Nonoverlapping (delta, gamma)-approximate pattern matchingIntelligent Data Analysis10.3233/IDA-21632526:6(1661-1682)Online publication date: 12-Nov-2022
https://doi.org/10.3233/IDA-216325
Gawrychowski PManea FSiemer S(2022)Matching Patterns with Variables Under Edit DistanceString Processing and Information Retrieval10.1007/978-3-031-20643-6_20(275-289)Online publication date: 1-Nov-2022
https://doi.org/10.1007/978-3-031-20643-6_20
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Published In

cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 12, Issue 1

March 2020

199 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/3376904

Editor:
Ryan O'Donnell
Carnegie Mellon University, USA

Issue’s Table of Contents

Copyright © 2020 ACM.

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Association for Computing Machinery

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Publication History

Published: 11 February 2020

Accepted: 01 September 2019

Revised: 01 August 2019

Received: 01 October 2018

Published in TOCT Volume 12, Issue 1

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Cited By

Fleischmann PKim SKoß TManea FNowotka DSiemer SWiedenhöft M(2023)Matching Patterns with Variables Under Simon’s CongruenceReachability Problems10.1007/978-3-031-45286-4_12(155-170)Online publication date: 5-Oct-2023
https://doi.org/10.1007/978-3-031-45286-4_12
Wu YJian BLi YJiang HWu X(2022)NetNDP: Nonoverlapping (delta, gamma)-approximate pattern matchingIntelligent Data Analysis10.3233/IDA-21632526:6(1661-1682)Online publication date: 12-Nov-2022
https://doi.org/10.3233/IDA-216325
Gawrychowski PManea FSiemer S(2022)Matching Patterns with Variables Under Edit DistanceString Processing and Information Retrieval10.1007/978-3-031-20643-6_20(275-289)Online publication date: 1-Nov-2022
https://doi.org/10.1007/978-3-031-20643-6_20
Monti ASinaimeri B(2020)String factorisations with maximum or minimum dimensionTheoretical Computer Science10.1016/j.tcs.2020.07.029842(65-73)Online publication date: Nov-2020
https://doi.org/10.1016/j.tcs.2020.07.029
Wu YFan JLi YGuo LWu X(2020)NetDAP: (δ, γ) −approximate pattern matching with length constraintsApplied Intelligence10.1007/s10489-020-01778-150:11(4094-4116)Online publication date: 10-Jul-2020
https://dl.acm.org/doi/10.1007/s10489-020-01778-1

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