English

Faster and simpler online/sliding rightmost Lempel-Ziv factorizations

Data Structures and Algorithms 2024-08-07 v1

Abstract

We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(n log n/log log n)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms.

Keywords

Cite

@article{arxiv.2408.03008,
  title  = {Faster and simpler online/sliding rightmost Lempel-Ziv factorizations},
  author = {Wataru Sumiyoshi and Takuya Mieno and Shunsuke Inenaga},
  journal= {arXiv preprint arXiv:2408.03008},
  year   = {2024}
}
R2 v1 2026-06-28T18:05:08.312Z