Online List Labeling with Near-Logarithmic Writes

TL;DR

This paper introduces a skip-list based algorithm for online list labeling that achieves near-logarithmic expected amortized writes per update, improving efficiency in dynamic ordered data management.

Contribution

It presents a novel skip-list based approach for online list labeling with near-logarithmic write complexity, a significant improvement over previous methods.

Findings

Expected amortized writes are $O(rac{1}{ ext{epsilon}} imes ext{log}(n) imes ext{poly}( ext{log} ext{log} n))$ per update.

The algorithm maintains order against an oblivious adversary efficiently.

Provides theoretical bounds on write complexity for dynamic list management.

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.