Lempel-Ziv Factorization Using Less Time & Space

For 30 years the Lempel-Ziv factorization LZx of a string x = x[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 LZx was based on Θ(n)-time (or, depending on the measure used, O(n log n)-time) processing of the suffix tree STx of x. Recently Abouelhoda et al. proposed an efficient Lempel-Ziv factorization algorithm based on an “enhanced” suffix array — that is, a suffix array SAx together with supporting data structures, principally an “interval tree”. In this paper we introduce a collection of fast spaceefficient 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. Mathematics Subject Classification (2000). Nonnumerical Algorithms 68W05.