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Journal Articles Journal of Computer and System Sciences Year : 2021

Circular pattern matching with k mismatches

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Abstract

The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic rotation of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic rotation of P. This is the circular pattern matching with k mismatches (k-CPM) problem. A multitude of papers have been devoted to solving this problem but, to the best of our knowledge, only average-case upper bounds are known. In this paper, we present the first non-trivial worst-case upper bounds for the k-CPM problem. Specifically, we show an O(nk)-time algorithm and an O(n + n m k 4)-time algorithm. The latter algorithm applies in an extended way a technique that was very recently developed for the k-mismatch problem [Bringmann et al., SODA 2019]. A preliminary version of this work appeared at FCT 2019. In this version we improve the time complexity of the main algorithm from O(n + n m k 5) to O(n + n m k 4).
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Dates and versions

hal-03498339 , version 1 (21-12-2021)

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Panagiotis Charalampopoulos, Tomasz Kociumaka, Solon P Pissis, Jakub Radoszewski, Wojciech Rytter, et al.. Circular pattern matching with k mismatches. Journal of Computer and System Sciences, 2021, 115, pp.73-85. ⟨10.1016/j.jcss.2020.07.003⟩. ⟨hal-03498339⟩

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