Indexing text using the Ziv-Lempel trie

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Abstract

Let a text of μ characters over an alphabet of size σ be compressible to n phrases by the LZ78 algorithm. We show how to build a data structure based on the Ziv-Lempel trie, called the LZ-index, that takes 4n log2 n(1 +o(1)) bits of space (that is, 4 times the entropy of the text for ergodic sources) and reports the R occurrences of a pattern of length m in worst case time O(m3 log2 + (m + R) log n). We present a practical implementation of the LZ-index, which is faster than current alternatives when we take into consideration the time to report the positions or text contexts of the occurrences found. © 2003 Elsevier B.V. All rights reserved.

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Navarro, G. (2004). Indexing text using the Ziv-Lempel trie. Journal of Discrete Algorithms, 2(1 SPEC. ISS.), 87–114. https://doi.org/10.1016/S1570-8667(03)00066-2

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