License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2019.29
URN: urn:nbn:de:0030-drops-105008
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10500/
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Urabe, Yuki ; Nakashima, Yuto ; Inenaga, Shunsuke ; Bannai, Hideo ; Takeda, Masayuki

On the Size of Overlapping Lempel-Ziv and Lyndon Factorizations

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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.

BibTeX - Entry

@InProceedings{urabe_et_al:LIPIcs:2019:10500,
  author =	{Yuki Urabe and Yuto Nakashima and Shunsuke Inenaga and Hideo Bannai and Masayuki Takeda},
  title =	{{On the Size of Overlapping Lempel-Ziv and Lyndon Factorizations}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{29:1--29:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Nadia Pisanti and Solon P. Pissis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10500},
  URN =		{urn:nbn:de:0030-drops-105008},
  doi =		{10.4230/LIPIcs.CPM.2019.29},
  annote =	{Keywords: Lyndon factorization, Lyndon words, Lempel-Ziv factorization}
}

Keywords: Lyndon factorization, Lyndon words, Lempel-Ziv factorization
Collection: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
Issue Date: 2019
Date of publication: 06.06.2019


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