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Subsequence Covers of Words

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String Processing and Information Retrieval (SPIRE 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13617))

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Abstract

We introduce subsequence covers (s-covers, in short), a new type of covers of a word. A word C is an s-cover of a word S if the occurrences of C in S as subsequences cover all the positions in S.

The s-covers seem to be computationally much harder than standard covers of words (cf. Apostolico et al., Inf. Process. Lett. 1991), but, on the other hand, much easier than the related shuffle powers (Warmuth and Haussler, J. Comput. Syst. Sci. 1984).

We give a linear-time algorithm for testing if a candidate word C is an s-cover of a word S over a polynomially-bounded integer alphabet. We also give an algorithm for finding a shortest s-cover of a word S, which in the case of a constant-sized alphabet, also runs in linear time. Furthermore, we complement our algorithmic results with a lower and an upper bound on the length of a longest word without non-trivial s-covers, which are both exponential in the size of the alphabet.

J. Radoszewski and T. Waleń—Supported by the Polish National Science Center, grant no. 2018/31/D/ST6/03991.

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Notes

  1. 1.

    The optimized C++ code used for the experiments can be found at https://www.mimuw.edu.pl/~jrad/code.cpp. The program reads k and computes \(\gamma (k)\); it finishes within 1 min for \(k \le 4\).

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Acknowledgements

We thank Juliusz Straszyński for his help in conducting computer experiments.

Author information

Authors and Affiliations

  1. Birkbeck, University of London, London, UK

    Panagiotis Charalampopoulos

  2. CWI, Amsterdam, The Netherlands

    Solon P. Pissis & Wiktor Zuba

  3. Vrije Universiteit, Amsterdam, The Netherlands

    Solon P. Pissis

  4. University of Warsaw, Warsaw, Poland

    Jakub Radoszewski, Wojciech Rytter & Tomasz Waleń

Authors
  1. Panagiotis Charalampopoulos
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  2. Solon P. Pissis
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  3. Jakub Radoszewski
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  4. Wojciech Rytter
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  5. Tomasz Waleń
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  6. Wiktor Zuba
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Corresponding author

Correspondence to Panagiotis Charalampopoulos .

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Editors and Affiliations

  1. Universidad Técnica Federico Santa María, Valparaíso, Chile

    Diego Arroyuelo

  2. Universidad de Chile, Santiago, Chile

    Barbara Poblete

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Charalampopoulos, P., Pissis, S.P., Radoszewski, J., Rytter, W., Waleń, T., Zuba, W. (2022). Subsequence Covers of Words. In: Arroyuelo, D., Poblete, B. (eds) String Processing and Information Retrieval. SPIRE 2022. Lecture Notes in Computer Science, vol 13617. Springer, Cham. https://doi.org/10.1007/978-3-031-20643-6_1

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  • DOI: https://doi.org/10.1007/978-3-031-20643-6_1

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