Faster and simpler online/sliding rightmost Lempel-Ziv factorizations
<|reference_start|>Faster and simpler online/sliding rightmost Lempel-Ziv factorizations: 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.<|reference_end|>
@article{sumiyoshi2024faster,
    title={Faster and simpler online/sliding rightmost Lempel-Ziv factorizations},
    author={Wataru Sumiyoshi, Takuya Mieno, and Shunsuke Inenaga},
    journal={arXiv preprint arXiv:2408.03008},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.03008},
    primaryClass={cs.DS}
}