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Lempel–Ziv Factorization Using Less Time & Space

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Abstract.

For 30 years the Lempel–Ziv factorization LZ x of a string xx[1..n] has been a fundamental data structure of string processing, especially valuable for string compression and for computing all the repetitions (runs) in x. Traditionally the standard method for computing LZ x was based on Θ(n)-time (or, depending on the measure used, O(n log n)-time) processing of the suffix tree ST x of x. Recently Abouelhoda et al. proposed an efficient Lempel–Ziv factorization algorithm based on an “enhanced” suffix array – that is, a suffix array SA x together with supporting data structures, principally an “interval tree”. In this paper we introduce a collection of fast space-efficient algorithms for LZ factorization, also based on suffix arrays, that in theory as well as in many practical circumstances are superior to those previously proposed; one family out of this collection achieves true Θ(n)-time alphabet-independent processing in the worst case by avoiding tree structures altogether.

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Correspondence to W. F. Smyth.

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The work of the first and third authors was supported in part by grants from the Natural Sciences & Engineering Research Council of Canada.

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Chen, G., Puglisi, S.J. & Smyth, W.F. Lempel–Ziv Factorization Using Less Time & Space. Math.comput.sci. 1, 605–623 (2008). https://doi.org/10.1007/s11786-007-0024-4

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  • DOI: https://doi.org/10.1007/s11786-007-0024-4

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