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.
@InProceedings{kopelowitz_et_al:OASIcs.SOSA.2018.10, author = {Kopelowitz, Tsvi and Porat, Ely}, title = {{A Simple Algorithm for Approximating the Text-To-Pattern Hamming Distance}}, booktitle = {1st Symposium on Simplicity in Algorithms (SOSA 2018)}, pages = {10:1--10:5}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-064-4}, ISSN = {2190-6807}, year = {2018}, volume = {61}, editor = {Seidel, Raimund}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2018.10}, URN = {urn:nbn:de:0030-drops-83089}, doi = {10.4230/OASIcs.SOSA.2018.10}, annote = {Keywords: Pattern Matching, Hamming Distance, Approximation Algorithms} }
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