Online List Labeling with Near-Logarithmic Writes

In the Online List Labeling problem, a set of $n\le N$ elements from a totally ordered universe must be stored in sorted order in an array with $m=N+\lceil \epsilon N\rceil$ slots, where $\epsilon \in (0,1]$ 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 $O({\epsilon }^{-1}\log (n)\mathrm{poly}(\log \log n))$ per update.