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.
N1 - Funding Information:
This research was partially supported by the Academy of Finland through grant 294143 and by the RFBR grant 16-01-00795.
Publisher Copyright:
© Juha Kärkkäinen, Dominik Kempa, Yuto Nakashima, Simon J. Puglisi, and Arseny M. Shur.
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.
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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
T2 - 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017
Y2 - 8 March 2017 through 11 March 2017
ER -