The k-Mappability Problem Revisited

Authors Amihood Amir, Itai Boneh, Eitan Kondratovsky

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Author Details

Amihood Amir
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
  • Georgia Tech, Atlanta, GA, USA
Itai Boneh
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
Eitan Kondratovsky
  • Department of Computer Science, Bar Ilan University, Ramat Gan, Israel
  • Cheriton School of Computer Science, Waterloo University, Waterloo, Canada


We warmly thank Tomasz Kociumaka for useful discussions.

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Amihood Amir, Itai Boneh, and Eitan Kondratovsky. The k-Mappability Problem Revisited. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Sorting and searching
  • Pattern Matching
  • Hamming Distance
  • Suffix Tree
  • Suffix Array


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