English

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.

Keywords

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}
}

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12 pages