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Two-Pattern Strings

  • František Franěk
  • Jiandong Jiang
  • Weilin Lu
  • William F. Smyth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2373)

Abstract

This paper introduces a new class of strings on {a, b}, called two-pattern strings, that constitute a substantial generalization of Sturmian strings while at the same time sharing many of their nice properties. In particular, we show that, in common with Sturmian strings, only time linear in the string length is required to recognize a two-pattern string as well as to compute all of its repetitions. We also show that two-pattern strings occur in some sense frequently in the class of all strings on {a,b}.

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References

  1. 1.
    M. Boshernitzan & Aviezri S. Fraenkel, A linear algorithm for nonhomogeneous spectra of numbers, J. Algorithms 5 (1984) 187–198.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Maxime Crochemore, An optimal algorithm for computing the repetitions in a word, IPL 12-5 (1981) 244–250.CrossRefMathSciNetGoogle Scholar
  3. 3.
    Martin Farach, Optimal suffix tree construction with large alphabets, Proc. 38th Annual IEEE Symp. FOCS (1997) 137–143.Google Scholar
  4. 4.
    Aviezri S. Fraenkel & R. Jamie Simpson, The exact number of squares in Fibonacci words, TCS 218-1 (1999) 83–94.Google Scholar
  5. 5.
    František Franěk, Ayşe Karaman & W. F. Smyth, Repetitions in Sturmian strings, TCS 249-2 (2000) 289–303.CrossRefGoogle Scholar
  6. 6.
    Leo J. Guibas & Andrew M. Odlyzko, Periods in strings, J. Combinatorial Theory, Series A 30 (1981) 19–42.CrossRefMathSciNetGoogle Scholar
  7. 7.
    Costas S. Iliopoulos, Dennis Moore & W. F. Smyth, A characterization of the squares in a Fibonacci string, TCS 172 (1997) 281–291.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Roman Kolpakov & Gregory Kucherov, On maximal repetitions in words, J. Discrete Algorithms 1 (2000) 159–186.MathSciNetGoogle Scholar
  9. 9.
    Abraham Lempel & Jacob Ziv, On the complexity of finite sequences, IEEE Trans. Information Theory 22 (1976) 75–81.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Michael G. Main, Detecting leftmost maximal periodicities, Discrete Applied Maths. 25 (1989) 145–153.CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Jacob Ziv & Abraham Lempel, A universal algorithm for sequential data compression, IEEE Trans. Information Theory 23 (1977) 337–343.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • František Franěk
    • 1
  • Jiandong Jiang
    • 1
    • 2
  • Weilin Lu
    • 1
    • 2
  • William F. Smyth
    • 1
    • 3
  1. 1.Algorithms Research Group, Department of Computing & SoftwareMcMaster UniversityHamiltonCanada
  2. 2.Toronto LaboratoriesIBM CanadaMarkhamCanada
  3. 3.School of ComputingCurtin UniversityPerthAustralia

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