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    Subsequence covers of words

    Charalampopoulos, Panagiotis and Pissis, S.P. and Radoszewski, J. and Rytter, W. and Waleń, T. and Zuba, W. (2022) Subsequence covers of words. Lecture Notes in Computer Science , pp. 3-15. ISSN 0302-9743.

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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.

    Metadata

    Item Type: Article
    Additional Information: International Symposium on String Processing and Information Retrieval. SPIRE 2022: String Processing and Information Retrieval, Proceedings. ISBN: 9783031206429
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Panagiotis Charalampopoulos
    Date Deposited: 30 Nov 2022 11:12
    Last Modified: 09 Aug 2023 12:54
    URI: https://eprints.bbk.ac.uk/id/eprint/49969

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