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Range Shortest Unique Substring Queries

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String Processing and Information Retrieval (SPIRE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11811))

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Abstract

Let \(\mathsf {T}[1,n]\) be a string of length n and \(\mathsf {T}[i,j]\) be the substring of \(\mathsf {T}\) starting at position i and ending at position j. A substring \(\mathsf {T}[i,j]\) of \(\mathsf {T}\) is a repeat if it occurs more than once in \(\mathsf {T}\); otherwise, it is a unique substring of \(\mathsf {T}\). Repeats and unique substrings are of great interest in computational biology and in information retrieval. Given string \(\mathsf {T}\) as input, the Shortest Unique Substring problem is to find a shortest substring of \(\mathsf {T}\) that does not occur elsewhere in \(\mathsf {T}\). In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over \(\mathsf {T}\) answering the following type of online queries efficiently. Given a range \([\alpha , \beta ]\), return a shortest substring \(\mathsf {T}[i,j]\) of \(\mathsf {T}\) with exactly one occurrence in \([\alpha , \beta ]\). We present an \(\mathcal {O}(n\log n)\)-word data structure with \(\mathcal {O}(\log _w n)\) query time, where \(w=\varOmega (\log n)\) is the word size. Our construction is based on a non-trivial reduction allowing us to apply a recently introduced optimal geometric data structure [Chan et al. ICALP 2018].

Supported in part by the U.S. National Science Foundation under CCF-1703489 and the Royal Society International Exchanges Scheme (IES\(\backslash \)R1\(\backslash \)180175).

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Authors and Affiliations

  1. Department of Computer Science, University of Central Florida, Orlando, USA

    Paniz Abedin & Sharma V. Thankachan

  2. Department of Computer Science, University of Wisconsin - Whitewater, Whitewater, USA

    Arnab Ganguly

  3. CWI, Amsterdam, The Netherlands

    Solon P. Pissis

Authors
  1. Paniz Abedin
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  2. Arnab Ganguly
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  3. Solon P. Pissis
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  4. Sharma V. Thankachan
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Correspondence to Paniz Abedin .

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Editors and Affiliations

  1. University of A Coruña, A Coruña, Spain

    Nieves R. Brisaboa

  2. University of Helsinki, Helsinki, Finland

    Simon J. Puglisi

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Abedin, P., Ganguly, A., Pissis, S.P., Thankachan, S.V. (2019). Range Shortest Unique Substring Queries. In: Brisaboa, N., Puglisi, S. (eds) String Processing and Information Retrieval. SPIRE 2019. Lecture Notes in Computer Science(), vol 11811. Springer, Cham. https://doi.org/10.1007/978-3-030-32686-9_18

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  • DOI: https://doi.org/10.1007/978-3-030-32686-9_18

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