The k-mappability problem revisited

Amihood Amir, Itai Boneh, Eitan Kondratovsky

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Abstract

The k-mappability problem has two integers parameters m and k. For every subword of size m in a text S, we wish to report the number of indices in S in which the word occurs with at most k mismatches. The problem was lately tackled by Alzamel et al. [1]. For a text with constant alphabet S and k ϵ O(1), they present an algorithm with linear space and O(n logk+1 n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(n log(n) log log(n)) time was presented in [2]. In this work, we enhance the techniques of [2] to obtain an algorithm with linear space and O(n log(n)) time for k = 1. Our algorithm removes the constraint of the alphabet being of constant size. We also present linear algorithms for the case of k = 1, |S| ϵ O(1) and m =Ω(√n).

Original languageEnglish
Title of host publication32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021
EditorsPawel Gawrychowski, Tatiana Starikovskaya
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771863
DOIs
StatePublished - 1 Jul 2021
Event32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021 - Wroclaw, Poland
Duration: 5 Jul 20217 Jul 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume191
ISSN (Print)1868-8969

Conference

Conference32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021
Country/TerritoryPoland
CityWroclaw
Period5/07/217/07/21

Bibliographical note

Funding Information:
Funding Amihood Amir: Partly supported by ISF grant 1475/18, BSF grant 2018141 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement No 683064. Itai Boneh: Partly supported by ISF grant 1475/75. Eitan Kondratovsky: Partly supported by ISF grant 1475/18.

Funding Information:
Amihood Amir: Partly supported by ISF grant 1475/18, BSF grant 2018141 and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme grant agreement No 683064 Partly supported by ISF grant 1475/75. Partly supported by ISF grant 1475/18.

Publisher Copyright:
© Amihood Amir, Itai Boneh, and Eitan Kondratovsky.

Keywords

  • Hamming Distance
  • Pattern Matching
  • Suffix Array
  • Suffix Tree

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