Longest Property-Preserved Common Factor

  • Lorraine A. K. Ayad
  • Giulia Bernardini
  • Roberto Grossi
  • Costas S. Iliopoulos
  • Nadia PisantiEmail author
  • Solon P. Pissis
  • Giovanna Rosone
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11147)


In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here we consider two fundamental string properties: square-free factors and periodic factors under two different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of on-line queries: given string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer \(1 < k'\le k\) and we are asked to find a longest periodic factor common to at least \(k'\) strings. We present linear-time solutions for both settings. We anticipate that our paradigm can be extended to other string properties.


Longest common factor Periodicity Squares Algorithms 



Solon P. Pissis and Giovanna Rosone are partially supported by the Royal Society project IE 161274 “Processing uncertain sequences: combinatorics and applications”. Giovanna Rosone and Nadia Pisanti are partially supported by the project Italian MIUR-SIR CMACBioSeq (“Combinatorial methods for analysis and compression of biological sequences”) grant n. RBSI146R5L.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lorraine A. K. Ayad
    • 1
  • Giulia Bernardini
    • 2
  • Roberto Grossi
    • 3
  • Costas S. Iliopoulos
    • 1
  • Nadia Pisanti
    • 3
    • 4
    Email author
  • Solon P. Pissis
    • 1
  • Giovanna Rosone
    • 3
  1. 1.Department of InformaticsKing’s College LondonLondonUK
  2. 2.Department of Informatics, Systems and CommunicationUniversity of Milan-BicoccaMilanItaly
  3. 3.Department of Computer ScienceUniversity of PisaPisaItaly
  4. 4.ERABLE TeamINRIALyonFrance

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