Near-Optimal Sublinear Time Algorithms for Ulam Distance

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 ˜O(d/R + √ d) 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-IndykKrauthgamer, SODA’09] and [Batu-Ergun-KilianMagen-Raskhodnikova-Rubinfeld-Sami, STOC’03].

• Type: Journal
• Year: 2010
• Where: SODA
• Authors: Alexandr Andoni, Huy L. Nguyen
• Keywords: Algorithms, Constant Approximation, Edit Distance, Lower Bounds, SODA 2010