Online List Labeling with Near-Logarithmic Writes

In the Online List Labeling problem, a set of n ≤ N elements from a totally ordered universe must be stored in sorted order in an array with m=N+ε N slots, where ε ∈ (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(ε⁻¹log (n) poly(log log n)) per update.