Longest Common Abelian Factors and Large Alphabets

  • Golnaz BadkobehEmail author
  • Travis Gagie
  • Szymon Grabowski
  • Yuto Nakashima
  • Simon J. Puglisi
  • Shiho Sugimoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9954)


Two strings X and Y are considered Abelian equal if the letters of X can be permuted to obtain Y (and vice versa). Recently, Alatabbi et al. (2015) considered the longest common Abelian factor problem in which we are asked to find the length of the longest Abelian-equal factor present in a given pair of strings. They provided an algorithm that uses \(O(\sigma n^2)\) time and \(O(\sigma n)\) space, where n is the length of the pair of strings and \(\sigma \) is the alphabet size. In this paper we describe an algorithm that uses \(O(n^2\log ^2n\log ^*n)\) time and \(O(n\log ^2n)\) space, significantly improving Alatabbi et al.’s result unless the alphabet is small. Our algorithm makes use of techniques for maintaining a dynamic set of strings under split, join, and equality testing (Melhorn et al., Algorithmica 17(2), 1997).


Suffix Tree Extra Space Alphabet Size Factor Length Alphabet Symbol 
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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Golnaz Badkobeh
    • 1
    Email author
  • Travis Gagie
    • 2
  • Szymon Grabowski
    • 3
  • Yuto Nakashima
    • 4
    • 5
  • Simon J. Puglisi
    • 2
  • Shiho Sugimoto
    • 4
  1. 1.Department of Computer ScienceUniversity of WarwickConventryUK
  2. 2.Department of Computer Science, Helsinki Institute for Information TechnologyUniversity of HelsinkiHelsinkiFinland
  3. 3.Institute of Applied Computer ScienceLodz University of TechnologyŁódźPoland
  4. 4.Department of InformaticsKyushu UniversityKyushuJapan
  5. 5.Japan Society for the Promotion of ScienceTokyoJapan

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