Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A sublinear algorithm for weakly approximating edit distance
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating the distance to a monotone function
Random Structures & Algorithms
The Computational Hardness of Estimating Edit Distance [Extended Abstract]
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The Smoothed Complexity of Edit Distance
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximating edit distance in near-linear time
Proceedings of the forty-first annual ACM symposium on Theory of computing
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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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 Õ(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-Indyk-Krauthgamer, SODA'09] and [Batu-Ergun-Kilian-Magen-Raskhodnikova-Rubinfeld-Sami, STOC'03].