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Generating Necklaces and Strings with Forbidden Substrings

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Book cover Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

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Abstract

Given a length m string f over a k-ary alphabet and a positive integer n, we develop efficient algorithms to generate

  1. (a)

    all k-ary strings of length n that have no substring equal to f,

  2. (b)

    all k-ary circular strings of length n that have no substring equal to f, and

  3. (c)

    all k-ary necklaces of length n that have no substring equal to f, where f is an aperiodic necklace.

Each of the algorithms runs in amortized time O(1) per string generated, independent of k, m, and n.

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References

  1. A. Aho, J. Hopcroft, and J. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

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  2. D. Gusfield, Algorithms on Strings, Trees, and Sequences, Cambridge University Press, 1997.

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  3. F. Ruskey, J. Sawada, An efficient algorithm for generating necklaces of fixed density, SIAM Journal on Computing, 29 (1999) 671–684.

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  4. F. Ruskey, J. Sawada, A fast algorithm to generate unlabeled necklaces, 11th Annual ACM-SIGACT Symposium on Discrete Algorithms (SODA), 2000, 256–262.

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  5. R.P. Stanley, Enumerative Combinatorics, Volume I, Wadsworth & Brooks/Cole, 1986.

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Author information

Authors and Affiliations

  1. University of Victoria, Victoria, B.C., V8W 3P6, Canada

    Frank Ruskey & Joe Sawada

Authors
  1. Frank Ruskey
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  2. Joe Sawada
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Ruskey, F., Sawada, J. (2000). Generating Necklaces and Strings with Forbidden Substrings. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_33

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  • DOI: https://doi.org/10.1007/3-540-44968-X_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

  • eBook Packages: Springer Book Archive

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