On the size of overlapping Lempel-Ziv and Lyndon factorizations

Yuki Urabe, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

Abstract

Lempel-Ziv (LZ) factorization and Lyndon factorization are well-known factorizations of strings. Recently, Kärkkäinen et al. studied the relation between the sizes of the two factorizations, and showed that the size of the Lyndon factorization is always smaller than twice the size of the non-overlapping LZ factorization [STACS 2017]. In this paper, we consider a similar problem for the overlapping version of the LZ factorization. Since the size of the overlapping LZ factorization is always smaller than the size of the non-overlapping LZ factorization and, in fact, can even be an O(log n) factor smaller, it is not immediately clear whether a similar bound as in previous work would hold. Nevertheless, in this paper, we prove that the size of the Lyndon factorization is always smaller than four times the size of the overlapping LZ factorization.

Original languageEnglish
Title of host publication30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019
EditorsNadia Pisanti, Solon P. Pissis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771030
DOIs
Publication statusPublished - Jun 1 2019
Event30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 - Pisa, Italy
Duration: Jun 18 2019Jun 20 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume128
ISSN (Print)1868-8969

Conference

Conference30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019
CountryItaly
CityPisa
Period6/18/196/20/19

All Science Journal Classification (ASJC) codes

  • Software

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  • Cite this

    Urabe, Y., Nakashima, Y., Inenaga, S., Bannai, H., & Takeda, M. (2019). On the size of overlapping Lempel-Ziv and Lyndon factorizations. In N. Pisanti, & S. P. Pissis (Eds.), 30th Annual Symposium on Combinatorial Pattern Matching, CPM 2019 [29] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 128). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.CPM.2019.29