Edit Distance in Near-Linear Time: it's a Constant Factor

We present an algorithm for approximating the edit distance between two strings of length n in time n^{1+\epsilon} , for any \epsilon > 0 , up to a constant factor. Our result completes a research direction set forth in the recent breakthrough paper [1], which showed the first constant-factor app...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 990 - 1001
Main Authors: Andoni, Alexandr, Nosatzki, Negev Shekel
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2020
Subjects:
Additives
Approximation algorithms
Complexity theory
edit distance
fine-grained complexity
Measurement
Signal processing algorithms
sublinear algorithms
Transforms
ISSN:2575-8454
Online Access:Get full text
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Summary:We present an algorithm for approximating the edit distance between two strings of length n in time n^{1+\epsilon} , for any \epsilon > 0 , up to a constant factor. Our result completes a research direction set forth in the recent breakthrough paper [1], which showed the first constant-factor approximation algorithm with a (strongly) sub-quadratic running time. The recent results [2], [3] have shown near-linear complexity only under the restriction that the edit distance is close to maximal (equivalently, there is a near-linear additive approximation). In contrast, our algorithm obtains a constant-factor approximation in near-linear running time for any input strings.
ISSN:2575-8454
DOI:10.1109/FOCS46700.2020.00096