On the Approximation Ratio of LZ-End to LZ77

Takumi Ideue, Takuya Mieno, Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings
EditorsThierry Lecroq, Hélène Touzet
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783030866914
Publication statusPublished - 2021
Event28th International Symposium on String Processing and Information Retrieval, SPIRE 2021 - Virtual, Online
Duration: Oct 4 2021Oct 6 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12944 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Symposium on String Processing and Information Retrieval, SPIRE 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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