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Conference on Computability in Europe

CiE 2015: Evolving Computability pp 313–323Cite as

Computing Equality-Free String Factorisations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9136))

Abstract

A factorisation of a string is equality-free if each two factors are different; its size is the number of factors and its width is the maximum length of any factor. To decide, for a string \(w\) and a number \(m\), whether \(w\) has an equality-free factorisation with a size of at least (or a width of at most) \(m\) are \(\mathrm {NP}\)-complete problems. We further investigate the complexity of these problems and also study the converse problems of computing a factorisation that is to a large extent not equality-free, i.e., a factorisation of size at least (or width at most) \(m\) such that the total number of different factors does not exceed a given bound \(k\).

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Notes

  1. 1.

    This problem is also mentioned in [1]; furthermore, in [6], the hardness of computing an equality-free factorisation with only palindromes as factors is investigated.

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Author information

Authors and Affiliations

  1. Fachbereich IV – Abteilung Informatikwissenschaften, Universität Trier, 54286, Trier, Germany

    Markus L. Schmid

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  1. Markus L. Schmid
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Correspondence to Markus L. Schmid .

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Editors and Affiliations

  1. Department of Computer Science, Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. University of Bucharest, Bucharest, Romania

    Victor Mitrana

  3. Sofia University, Sofia, Bulgaria

    Mariya Soskova

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© 2015 Springer International Publishing Switzerland

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Schmid, M.L. (2015). Computing Equality-Free String Factorisations. In: Beckmann, A., Mitrana, V., Soskova, M. (eds) Evolving Computability. CiE 2015. Lecture Notes in Computer Science(), vol 9136. Springer, Cham. https://doi.org/10.1007/978-3-319-20028-6_32

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  • DOI: https://doi.org/10.1007/978-3-319-20028-6_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20027-9

  • Online ISBN: 978-3-319-20028-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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