Efficiently finding all maximal α-gapped repeats

Paweł Gawrychowski, Tomohiro I, Shunsuke Inenaga, Dominik Köppl, Florin Manea

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

For α ≥ 1, an α-gapped repeat in a word w is a factor uvu of w such that |uv| ≤ α|u|; the two occurrences of a factor u in such a repeat are called arms. Such a repeat is called maximal if its arms cannot be extended simultaneously with the same symbol to the right nor to the left. We show that the number of all maximal α-gapped repeats occurring in words of length n is upper bounded by 18αn, allowing us to construct an algorithm finding all maximal α-gapped repeats of a word on an integer alphabet of size nO(1); in O(αn) time. This result is optimal as there are words that have Θ(αn) maximal α-gapped repeats. Our techniques can be extended to get comparable results in the case of α-gapped palindromes, i.e., factors uvuT with |uv| ≤ α|u|.

Original languageEnglish
Title of host publication33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
EditorsHeribert Vollmer, Nicolas Ollinger
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770019
DOIs
Publication statusPublished - Feb 1 2016
Event33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 - Orleans, France
Duration: Feb 17 2016Feb 20 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume47
ISSN (Print)1868-8969

Other

Other33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
CountryFrance
CityOrleans
Period2/17/162/20/16

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Gawrychowski, P., I, T., Inenaga, S., Köppl, D., & Manea, F. (2016). Efficiently finding all maximal α-gapped repeats. In H. Vollmer, & N. Ollinger (Eds.), 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 [39] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 47). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2016.39