License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2021.5
URN: urn:nbn:de:0030-drops-139566
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13956/
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Amir, Amihood ; Boneh, Itai ; Kondratovsky, Eitan

The k-Mappability Problem Revisited

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LIPIcs-CPM-2021-5.pdf (0.7 MB)

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. [Mai Alzamel et al., 2018]. For a text with constant alphabet Σ and k ∈ O(1), they present an algorithm with linear space and O(nlog^{k+1}n) time. For the case in which k = 1 and a constant size alphabet, a faster algorithm with linear space and O(nlog(n)log log(n)) time was presented in [Mai Alzamel et al., 2020].
In this work, we enhance the techniques of [Mai Alzamel et al., 2020] 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, |Σ| ∈ O(1) and m = Ω(√n).

BibTeX - Entry

@InProceedings{amir_et_al:LIPIcs.CPM.2021.5,
  author =	{Amir, Amihood and Boneh, Itai and Kondratovsky, Eitan},
  title =	{{The k-Mappability Problem Revisited}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13956},
  URN =		{urn:nbn:de:0030-drops-139566},
  doi =		{10.4230/LIPIcs.CPM.2021.5},
  annote =	{Keywords: Pattern Matching, Hamming Distance, Suffix Tree, Suffix Array}
}

Keywords: Pattern Matching, Hamming Distance, Suffix Tree, Suffix Array
Collection: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
Issue Date: 2021
Date of publication: 30.06.2021

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