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A Simple Algorithm for Approximating the Text-To-Pattern Hamming Distance

Authors Tsvi Kopelowitz, Ely Porat

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  • Pattern Matching
  • Hamming Distance
  • Approximation Algorithms

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Abstract

The algorithmic task of computing the Hamming distance between a given pattern of length m and each location in a text of length n, both over a general alphabet \Sigma, is one of the most fundamental algorithmic tasks in string algorithms. The fastest known runtime for exact computation is \tilde O(n\sqrt m). We recently introduced a complicated randomized algorithm for obtaining a (1 +/- eps) approximation for each location in the text in O( (n/eps) log(1/eps) log n log m log |\Sigma|) total time, breaking a barrier that stood for 22 years. In this paper, we introduce an elementary and simple randomized algorithm that takes O((n/eps) log n log m) time.

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Tsvi Kopelowitz and Ely Porat. A Simple Algorithm for Approximating the Text-To-Pattern Hamming Distance. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 10:1-10:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/OASIcs.SOSA.2018.10

Author Details

Tsvi Kopelowitz
Ely Porat

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