Finding Maximal Pairs with Bounded Gap

Gerth Stølting Brodal, Rune Bang Lyngsø, Christian Nørgaard Storm Pedersen, and Jens Stoye

In Proc. 10th Annual Symposium on Combinatorial Pattern Matching, volume 1645 of Lecture Notes in Computer Science, pages 134-149. Springer Verlag, Berlin, 1999.


A pair in a string is the occurrence of the same substring twice. A pair is maximal if the two occurrences of the substring cannot be extended to the left and right without making them different. The gap of a pair is the number of characters between the two occurrences of the substring. In this paper we present methods for finding all maximal pairs under various constraints on the gap. In a string of length n we can find all maximal pairs with gap in an upper and lower bounded interval in time O(n log n + z) where z is the number of reported pairs. If the upper bound is removed the time reduces to O(n + z). Since a tandem repeat is a pair where the gap is zero, our methods can be seen as a generalization of finding tandem repeats. The running time of our methods equals the running time of well known methods for finding tandem repeats.

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© Springer-Verlag Berlin Heidelberg 1999. All rights reserved.

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BIBTEX entry

  author = "Gerth St{\o}lting Brodal and Rune Bang Lyngs{\o} and Christian N{\o}rgaard Storm Pedersen and Jens Stoye",
  booktitle = "Proc. 10th Annual Symposium on Combinatorial Pattern Matching",
  doi = "10.1007/3-540-48452-3_11",
  isbn = "978-3-540-66278-5",
  pages = "134-149",
  publisher = "Springer {V}erlag, Berlin",
  series = "Lecture Notes in Computer Science",
  title = "Finding Maximal Pairs with Bounded Gap",
  volume = "1645",
  year = "1999"