On the size of Lempel-Ziv and Lyndon factorizations

Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, Arseny M. Shur

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

4 Citations (Scopus)

Abstract

Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is always less than twice the size.

Original languageEnglish
Title of host publication34th Symposium on Theoretical Aspects of Computer Science, STACS 2017
EditorsBrigitte Vallee, Heribert Vollmer
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770286
DOIs
Publication statusPublished - Mar 1 2017
Event34th Symposium on Theoretical Aspects of Computer Science, STACS 2017 - Hannover, Germany
Duration: Mar 8 2017Mar 11 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume66
ISSN (Print)1868-8969

Other

Other34th Symposium on Theoretical Aspects of Computer Science, STACS 2017
CountryGermany
CityHannover
Period3/8/173/11/17

Fingerprint

Factorization

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Kärkkäinen, J., Kempa, D., Nakashima, Y., Puglisi, S. J., & Shur, A. M. (2017). On the size of Lempel-Ziv and Lyndon factorizations. In B. Vallee, & H. Vollmer (Eds.), 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017 [45] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 66). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2017.45

On the size of Lempel-Ziv and Lyndon factorizations. / Kärkkäinen, Juha; Kempa, Dominik; Nakashima, Yuto; Puglisi, Simon J.; Shur, Arseny M.

34th Symposium on Theoretical Aspects of Computer Science, STACS 2017. ed. / Brigitte Vallee; Heribert Vollmer. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. 45 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 66).

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

Kärkkäinen, J, Kempa, D, Nakashima, Y, Puglisi, SJ & Shur, AM 2017, On the size of Lempel-Ziv and Lyndon factorizations. in B Vallee & H Vollmer (eds), 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017., 45, Leibniz International Proceedings in Informatics, LIPIcs, vol. 66, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, Hannover, Germany, 3/8/17. https://doi.org/10.4230/LIPIcs.STACS.2017.45
Kärkkäinen J, Kempa D, Nakashima Y, Puglisi SJ, Shur AM. On the size of Lempel-Ziv and Lyndon factorizations. In Vallee B, Vollmer H, editors, 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2017. 45. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.STACS.2017.45
Kärkkäinen, Juha ; Kempa, Dominik ; Nakashima, Yuto ; Puglisi, Simon J. ; Shur, Arseny M. / On the size of Lempel-Ziv and Lyndon factorizations. 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017. editor / Brigitte Vallee ; Heribert Vollmer. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2017. (Leibniz International Proceedings in Informatics, LIPIcs).
@inproceedings{00dfe5d46e844d65b96643b35037d49c,
title = "On the size of Lempel-Ziv and Lyndon factorizations",
abstract = "Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is always less than twice the size.",
author = "Juha K{\"a}rkk{\"a}inen and Dominik Kempa and Yuto Nakashima and Puglisi, {Simon J.} and Shur, {Arseny M.}",
year = "2017",
month = "3",
day = "1",
doi = "10.4230/LIPIcs.STACS.2017.45",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Brigitte Vallee and Heribert Vollmer",
booktitle = "34th Symposium on Theoretical Aspects of Computer Science, STACS 2017",

}

TY - GEN

T1 - On the size of Lempel-Ziv and Lyndon factorizations

AU - Kärkkäinen, Juha

AU - Kempa, Dominik

AU - Nakashima, Yuto

AU - Puglisi, Simon J.

AU - Shur, Arseny M.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is always less than twice the size.

AB - Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct connection between the two by showing that while the Lyndon factorization can be bigger than the non-overlapping LZ factorization (which we demonstrate by describing a new, non-trivial family of strings) it is always less than twice the size.

UR - http://www.scopus.com/inward/record.url?scp=85016179442&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016179442&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.STACS.2017.45

DO - 10.4230/LIPIcs.STACS.2017.45

M3 - Conference contribution

AN - SCOPUS:85016179442

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017

A2 - Vallee, Brigitte

A2 - Vollmer, Heribert

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -