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Reducing the Space Requirement of LZ-Index

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Combinatorial Pattern Matching (CPM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4009))

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Abstract

The LZ-index is a compressed full-text self-index able to represent a text P 1...m, over an alphabet of size \(\sigma = O(\textrm{polylog}(u))\) and with k-th order empirical entropy H k (T), using 4uH k (T) + o(ulogσ) bits for any k = o(log σ u). It can report all the occ occurrences of a pattern P 1...m in T in O(m 3logσ + (m + occ)logu) worst case time. Its main drawback is the factor 4 in its space complexity, which makes it larger than other state-of-the-art alternatives. In this paper we present two different approaches to reduce the space requirement of LZ-index. In both cases we achieve (2 + ε)uH k (T) + o(ulogσ) bits of space, for any constant ε> 0, and we simultaneously improve the search time to O(m 2logm + (m + occ)logu). Both indexes support displaying any subtext of length ℓ in optimal O(ℓ/log σ u) time. In addition, we show how the space can be squeezed to (1 + ε)uH k (T) + o(ulogσ) to obtain a structure with O(m 2) average search time for \(m \geqslant 2\log_\sigma{u}\).

Supported in part by CONICYT PhD Fellowship Program (first author) and Fondecyt Grant 1-050493 (second author) and the Grant-in-Aid of the Ministry of Education, Science, Sports and Culture of Japan (third author).

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Universidad de Chile,  

    Diego Arroyuelo & Gonzalo Navarro

  2. Dept. of Computer Science and Communication Engineering, Kyushu University, Japan

    Kunihiko Sadakane

Authors
  1. Diego Arroyuelo
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  2. Gonzalo Navarro
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  3. Kunihiko Sadakane
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Moshe Lewenstein

  2. Department of Software, Technical University of Catalonia, 08034, Barcelona, Spain

    Gabriel Valiente

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© 2006 Springer-Verlag Berlin Heidelberg

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Arroyuelo, D., Navarro, G., Sadakane, K. (2006). Reducing the Space Requirement of LZ-Index. In: Lewenstein, M., Valiente, G. (eds) Combinatorial Pattern Matching. CPM 2006. Lecture Notes in Computer Science, vol 4009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780441_29

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  • DOI: https://doi.org/10.1007/11780441_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35455-0

  • Online ISBN: 978-3-540-35461-1

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