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Fast and practical algorithms for computing all the runs in a string
Journal article   Peer reviewed

Fast and practical algorithms for computing all the runs in a string

G. Chen, S.J. Puglisi and W.F. Smyth
Combinatorial Pattern Matching, Vol.4580, pp.307-315
2007
DOI: https://doi.org/10.1007/978-3-540-73437-6_31
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Abstract

A repetition in a string x is a substring w=ue of x, maximum e ≥ 2, where u is not itself a repetition in w. A run in x is a substring w=ueu∗ of “maximal periodicity”, where ue is a repetition and u * a maximum-length possibly empty proper prefix of u. A run may encode as many as |u| repetitions. The maximum number of repetitions in any string x=x[1..n] is well known to be Θ(nlogn). In 2000 Kolpakov & Kucherov showed that the maximum number of runs in x is O(n); they also described a Θ(n)-time algorithm, based on Farach’s Θ(n)-time suffix tree construction algorithm (STCA), Θ(n)-time Lempel-Ziv factorization, and Main’s Θ(n)-time leftmost runs algorithm, to compute all the runs in x. Recently Abouelhoda et al. proposed a Θ(n)-time Lempel-Ziv factorization algorithm based on an “enhanced” suffix array — a suffix array together with other supporting data structures. In this paper we introduce a collection of fast space-efficient algorithms for computing all the runs in a string that appear in many circumstances to be superior to those previously proposed.

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