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Online List Labeling with Near-Logarithmic Writes (2405.04467v1)

Published 7 May 2024 in cs.DS

Abstract: 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.

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