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The Cartographer
Faster and simpler online/sliding rightmost Lempel-Ziv factorizations
August 06, 2024 Β· Declared Dead Β· π SPIRE
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Authors
Wataru Sumiyoshi, Takuya Mieno, Shunsuke Inenaga
arXiv ID
2408.03008
Category
cs.DS: Data Structures & Algorithms
Citations
2
Venue
SPIRE
Last Checked
4 months ago
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.
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