Online List Labeling with Near-Logarithmic Writes
<|reference_start|>Online List Labeling with Near-Logarithmic Writes: In the Online List Labeling problem, a set of $n \leq N$ elements from a totally ordered universe must be stored in sorted order in an array with $m=N+\lceil\varepsilon N \rceil$ slots, where $\varepsilon \in (0,1]$ is constant, while an adversary chooses elements that must be inserted and deleted from the set.   We devise a skip-list based algorithm for maintaining order against an oblivious adversary and show that the expected amortized number of writes is $O(\varepsilon^{-1}\log (n) \operatorname{poly}(\log \log n))$ per update.<|reference_end|>
@article{seybold2024online,
    title={Online List Labeling with Near-Logarithmic Writes},
    author={Martin P. Seybold},
    journal={arXiv preprint arXiv:2405.04467},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.04467},
    primaryClass={cs.DS}
}