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Maintaining the Size of LZ77 on Semi-Dynamic Strings

Authors Hideo Bannai , Panagiotis Charalampopoulos , Jakub Radoszewski

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Data compression
Keywords
  • Lempel-Ziv
  • compression
  • LZ77
  • semi-dynamic algorithm
  • cyclic rotation

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Abstract

We consider the problem of maintaining the size of the LZ77 factorization of a string S of length at most n under the following operations: (a) appending a given letter to S and (b) deleting the first letter of S. Our main result is an algorithm for this problem with amortized update time Õ(√n). As a corollary, we obtain an Õ(n√n)-time algorithm for computing the most LZ77-compressible rotation of a length-n string - a naive approach for this problem would compute the LZ77 factorization of each possible rotation and would thus take quadratic time in the worst case. We also show an Ω(√n) lower bound for the additive sensitivity of LZ77 with respect to the rotation operation. Our algorithm employs dynamic trees to maintain the longest-previous-factor array information and depends on periodicity-based arguments that bound the number of the required updates and enable their efficient computation.

Cite As Get BibTex

Hideo Bannai, Panagiotis Charalampopoulos, and Jakub Radoszewski. Maintaining the Size of LZ77 on Semi-Dynamic Strings. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CPM.2024.3

Author Details

Hideo Bannai
  • M&D Data Science Center, Tokyo Medical and Dental University (TMDU), Japan
Panagiotis Charalampopoulos
  • Birkbeck, University of London, UK
Jakub Radoszewski
  • Institute of Informatics, University of Warsaw, Poland

Funding

  • Bannai, Hideo: JSPS KAKENHI Grant Number JP20H04141.
  • Radoszewski, Jakub: Supported by the Polish National Science Center, grant no. 2022/46/E/ST6/00463.

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