Locating maximal approximate runs in a string

Mika Amit, Maxime Crochemore, Gad M. Landau, Dina Sokol

Research output: Contribution to journalArticlepeer-review


An exact run in a string T is a non-empty substring of T that is a repetition of a smaller substring possibly followed by a prefix of it. Finding maximal exact runs in strings is an important problem and therefore a well-studied one in the area of stringology. For a given string T of length n, finding all maximal exact runs in the string can be done in O(nlog⁡n) time on general ordered alphabets or O(n) time on integer alphabets. In this paper, we investigate the maximal approximate runs problem: for a given string T and a number k, find non-empty substrings T of T such that changing at most k letters in T transforms them into a maximal exact run. We present an O(nk2log2⁡k+occ) algorithm to solve this problem, where occ is the number of substrings found.

Original languageEnglish
Pages (from-to)45-62
Number of pages18
JournalTheoretical Computer Science
StatePublished - 14 Nov 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.


  • Algorithms on strings
  • Pattern matching
  • Repetitions
  • Runs
  • Tandem repeats

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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