Periods in Partial Words: An Algorithm

  • Francine Blanchet-Sadri
  • Travis Mandel
  • Gautam Sisodia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)


Partial words are finite sequences over a finite alphabet that may contain some holes. A variant of the celebrated Fine-Wilf theorem shows the existence of a bound L = L(h,p,q) such that if a partial word of length at least L with h holes has periods p and q, then it has period \(\gcd(p,q)\). In this paper, we associate a graph with each p- and q-periodic word, and study two types of vertex connectivity on such a graph: modified degree connectivity and r-set connectivity where \(r = q \bmod{p}\). As a result, we give an algorithm for computing L(h, p, q) in the general case.


Optimal Length Repeated Pattern Closed Formula Vertex Connectivity Partial Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Travis Mandel
    • 2
  • Gautam Sisodia
    • 3
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsThe University of TexasAustinUSA
  3. 3.Department of MathematicsUniversity of WashingtonSeattleUSA

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