FMMS_2015_TOCT.pdf (900.21 kB)
Pattern matching with variables: Efficient algorithms and complexity results
journal contribution
posted on 2019-10-29, 16:45 authored by Henning Fernau, Florin Manea, Robert MercasRobert Mercas, Markus SchmidA pattern α (i. e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of α 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 clases of patterns.
Funding
DFG grant MA 5725/1-2 (project number 218587403)
History
School
- Science
Department
- Computer Science
Published in
ACM Transactions on Computation TheoryVolume
12Issue
1Publisher
Association for Computing MachineryVersion
- AM (Accepted Manuscript)
Rights holder
© Association for Computing MachineryPublisher statement
© ACM 2020. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Computation Theory, https://doi.org/10.1145/3369935.Acceptance date
2019-10-21Publication date
2020-02-11Copyright date
2020Notes
This is the author's version of the work created using a standard ACM template using dummy details, i.e., journal title, vol, issue, article number, publication, doi. The citation on the template should be ignored. The correct citation details are in the record metadata.ISSN
1942-3454eISSN
1942-3462Publisher version
Language
- en