On the Size of Lempel-Ziv and Lyndon Factorizations
Data Structures and Algorithms
2020-12-08 v1 Discrete Mathematics
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 never more than twice the size.
Cite
@article{arxiv.1611.08898,
title = {On the Size of Lempel-Ziv and Lyndon Factorizations},
author = {Juha Kärkkäinen and Dominik Kempa and Yuto Nakashima and Simon J. Puglisi and Arseny M. Shur},
journal= {arXiv preprint arXiv:1611.08898},
year = {2020}
}
Comments
12 pages