On the Size of Lempel-Ziv and Lyndon Factorizations

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

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

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Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, and Arseny M. Shur. On the Size of Lempel-Ziv and Lyndon Factorizations. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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.
  • Lempel-Ziv factorization
  • Lempel-Ziv parsing
  • LZ
  • Lyndon word
  • Lyndon factorization
  • Standard factorization


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