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Annual Symposium on Combinatorial Pattern Matching

CPM 2015: Combinatorial Pattern Matching pp 316–328Cite as

Tighter Bounds for the Sum of Irreducible LCP Values

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

Abstract

The suffix array is frequently augmented with the longest-common-prefix (LCP) array that stores the lengths of the longest common prefixes between lexicographically adjacent suffixes of a text. While the sum of the values in the LCP array can be \(\Omega (n^2)\) for a text of length \(n\), the sum of so-called irreducible LCP values was shown to be \(\mathcal {O}(n\lg n)\) just a few years ago. In this paper, we improve the bound to \(\mathcal {O}(n\lg r)\), where \(r\le n\) is the number of runs in the Burrows-Wheeler transform of the text. We also show that our bound is tight up to lower order terms (unlike the previous bound). Our results and the techniques used in proving them provide new insights into the combinatorics of text indexing and compression, and have immediate applications to LCP array construction algorithms.

Partially supported by the project “Enhancing Educational Potential of Nicolaus Copernicus University” (project no. POKL.04.01.01-00-081/10).

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Notes

  1. 1.

    Throughout the paper we use \(\lg \) as a shorthand for \(\log _2\).

  2. 2.

    We use the double brace notation \(\{\!\!\{{\cdot }\}\!\!\}\) to denote a multiset as opposed to a set.

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Author information

Authors and Affiliations

  1. Helsinki Institute of Information Technology (HIIT) and Department of Computer Science, University of Helsinki, Helsinki, Finland

    Juha Kärkkäinen, Dominik Kempa & Marcin Piątkowski

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Torun, Poland

    Marcin Piątkowski

Authors
  1. Juha Kärkkäinen
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  2. Dominik Kempa
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  3. Marcin Piątkowski
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Corresponding author

Correspondence to Juha Kärkkäinen .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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© 2015 Springer International Publishing Switzerland

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Kärkkäinen, J., Kempa, D., Piątkowski, M. (2015). Tighter Bounds for the Sum of Irreducible LCP Values. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_27

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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