Fast, Practical Algorithms for Computing All the Repeats in a String
Access Status
Authors
Date
2010Type
Metadata
Show full item recordAbstract
Given a string x = x[1..n] on an alphabet of size α, and a threshold p min ≥ 1, we describe four variants of an algorithm PSY1 that, using a suffix array, computes all the complete nonextendible repeats in x of length p ≥ p min . The basic algorithm PSY1–1 and its simple extension PSY1–2 are fast on strings that occur in biological, natural language and other applications (not highly periodic strings), while PSY1–3 guarantees Θ(n) worstcase execution time. The final variant, PSY1–4, also achieves Θ(n) processing time and, over the complete range of strings tested, is the fastest of the four. The space requirement of all four algorithms is about 5n bytes, but all make use of the “longest common prefix” (LCP) array, whose construction requires about 6n bytes. The four algorithms are faster in applications and use less space than a recentlyproposed algorithm (Narisawa in Proceedings of 18th Annual Symposium on Combinatorial Pattern Matching, pp. 340–351, 2007) that produces equivalent output. The suffix array is not explicitly used by algorithms PSY1, but may be required for postprocessing; in this case, storage requirements rise to 9n bytes. We also describe two variants of a fast Θ(n)time algorithm PSY2 for computing all complete supernonextendible repeats in x.
Citation
Source Title
Department
Remarks
The original publication is available at http://www.springerlink.com
Collections
Related items
Showing items related by title, author, creator and subject.

Franek, F.; Smyth, Bill (2004)Recently, several authors presented linear recursive algorithms for sorting suffixes of a string. All these algorithms employ a similar threestep approach, based on an initial division of the suffixes of x into two sets: ...

Iliopoulos, Costas; Smyth, Bill; Yusufu, M. (2009)A repeat in a string is a substring that occurs more than once. A repeat is extendible if every occurrence of the repeat has an identical letter either on the left or on the right; otherwise, it is maximal. A multirepeat ...

Puglisi, Simon; Smyth, Bill; Yusufu, M. (2008)Given a string x = x[1..n] on an alphabet of size a, and a threshold pmin = 1, we first describe a new algorithm PSY1 that, based on suffix array construction, computes all the complete nonextendible repeats in x of length ...