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Periods in Partial Words: An Algorithm

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Combinatorial Algorithms (IWOCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7056))

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Abstract

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.

This material is based upon work supported by the National Science Foundation under Grant No. DMS–0452020.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC, 27402–6170, USA

    Francine Blanchet-Sadri

  2. Department of Mathematics, The University of Texas, 1 University Station, C1200, Austin, TX, 78712, USA

    Travis Mandel

  3. Department of Mathematics, University of Washington, P.O. Box 354350, Seattle, WA, 98195-4350, USA

    Gautam Sisodia

Authors
  1. Francine Blanchet-Sadri
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  2. Travis Mandel
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  3. Gautam Sisodia
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Editor information

Editors and Affiliations

  1. Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia

    Costas S. Iliopoulos

  2. Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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© 2011 Springer-Verlag Berlin Heidelberg

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Blanchet-Sadri, F., Mandel, T., Sisodia, G. (2011). Periods in Partial Words: An Algorithm. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-25011-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25010-1

  • Online ISBN: 978-3-642-25011-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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