On the approximation ratio of LZ-End to LZ77
Abstract
A family of Lempel-Ziv factorizations is a well-studied string structure. The LZ-End factorization is a member of the family that achieved faster extraction of any substrings (Kreft & Navarro, TCS 2013). One of the interests for LZ-End factorizations is the possible difference between the size of LZ-End and LZ77 factorizations. They also showed families of strings where the approximation ratio of the number of LZ-End phrases to the number of LZ77 phrases asymptotically approaches 2. However, the alphabet size of these strings is unbounded. In this paper, we analyze the LZ-End factorization of the period-doubling sequence. We also show that the approximation ratio for the period-doubling sequence asymptotically approaches 2 for the binary alphabet.
Keywords
Cite
@article{arxiv.2106.01173,
title = {On the approximation ratio of LZ-End to LZ77},
author = {Takumi Ideue and Takuya Mieno and Mitsuru Funakoshi and Yuto Nakashima and Shunsuke Inenaga and Masayuki Takeda},
journal= {arXiv preprint arXiv:2106.01173},
year = {2021}
}