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Approximating Longest Common Substring with k mismatches: Theory and Practice

Authors Garance Gourdel, Tomasz Kociumaka , Jakub Radoszewski , Tatiana Starikovskaya

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Author Details

Garance Gourdel
  • ENS Paris Saclay, France
Tomasz Kociumaka
  • Bar-Ilan University, Ramat Gan, Israel
Jakub Radoszewski
  • Institute of Informatics, University of Warsaw, Poland
  • Samsung R&D Institute, Warsaw, Poland
Tatiana Starikovskaya
  • DIENS, École normale supérieure, PSL Research University, France

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Garance Gourdel, Tomasz Kociumaka, Jakub Radoszewski, and Tatiana Starikovskaya. Approximating Longest Common Substring with k mismatches: Theory and Practice. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 16:1-16:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


In the problem of the longest common substring with k mismatches we are given two strings X, Y and must find the maximal length 𝓁 such that there is a length-𝓁 substring of X and a length-𝓁 substring of Y that differ in at most k positions. The length 𝓁 can be used as a robust measure of similarity between X, Y. In this work, we develop new approximation algorithms for computing 𝓁 that are significantly more efficient that previously known solutions from the theoretical point of view. Our approach is simple and practical, which we confirm via an experimental evaluation, and is probably close to optimal as we demonstrate via a conditional lower bound.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • approximation algorithms
  • string similarity
  • LSH
  • conditional lower bounds


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