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On Extended Special Factors of a Word

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Book cover String Processing and Information Retrieval (SPIRE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11147))

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Abstract

An extended special factor of a word x is a factor of x whose longest infix can be extended by at least two distinct letters to the left or to the right and still occur in x. It is called extended bispecial if it can be extended in both directions and still occur in x. Let \(\rho (n)\) be the maximum number of extended bispecial factors over all words of length n. Almirantis et al. have shown that \(2n - 6 \le \rho (n) \le 3n-4\) [WABI 2017]. In this article, we show that there is no constant \(c<3\) such that \(\rho (n) \le cn\). We then exploit the connection between extended special factors and minimal absent words to construct a data structure for computing minimal absent words of a specific length in optimal time for integer alphabets generalising a result by Fujishige et al. [MFCS 2016]. As an application of our data structure, we show how to compare two words over an integer alphabet in optimal time improving on another result by Charalampopoulos et al. [Inf. Comput. 2018].

P. Charalampopoulos—Partially supported by a Studentship from the Faculty of Natural and Mathematical Sciences at King’s College London and an A. G. Leventis Foundation Educational Grant.

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Notes

  1. 1.

    In this case, x is called closed. Such words are an object of combinatorial interest [21].

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Acknowledgements

The authors would like to acknowledge the financial support towards travel and subsistence from the Laboratoire d’Informatique Gaspard-Monge at the Université Paris-Est, where part of this work has been conducted.

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Authors and Affiliations

  1. Department of Informatics, King’s College London, London, UK

    Panagiotis Charalampopoulos, Maxime Crochemore & Solon P. Pissis

  2. Université Paris-Est, Marne-la-Vallée, France

    Maxime Crochemore

Authors
  1. Panagiotis Charalampopoulos
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  2. Maxime Crochemore
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  3. Solon P. Pissis
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Correspondence to Solon P. Pissis .

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Editors and Affiliations

  1. Diego Portales University, Santiago, Chile

    Travis Gagie

  2. The University of Melbourne, Melbourne, VIC, Australia

    Alistair Moffat

  3. University of Chile, Santiago, Chile

    Gonzalo Navarro

  4. Universidad de Ingeniería y Tecnología, Lima, Peru

    Ernesto Cuadros-Vargas

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Charalampopoulos, P., Crochemore, M., Pissis, S.P. (2018). On Extended Special Factors of a Word. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_11

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  • DOI: https://doi.org/10.1007/978-3-030-00479-8_11

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