Near-Optimal Sublinear Time Algorithms for Ulam Distance
Alexandr Andoni, Huy Lê Nguyễn · 2010
We give near-tight bounds for estimating the edit distance between two non-repetitive strings (Ulam distance) with constant approximation, in sub-linear time. For two strings of length d and at edit distance R, our algorithm runs in time and outputs a constant approximation to R. We also prove a matching lower bound (up to logarithmic terms). Both upper and lower bounds are improvements over previous results from, respectively, [Andoni-Indyk-Krauthgamer, SODA'09] and [Batu-Ergun-Kilian-Magen-Raskhodnikova-Rubinfeld-Sami, STOC'03].