An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Text algorithms
Handbook of formal languages, vol. 1
Information-Theoretic Limitations of Formal Systems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The macro model for data compression (Extended Abstract)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On average sequence complexity
Theoretical Computer Science
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With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, r(w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu . . . u of the same subword u of w are stored as (u, n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, sub, and Lempel-Ziv complexity, lz. We have always r(w) = lz(w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word a being ultimately periodic is equivalent to: (i) sub(prefn(驴)) = O(n), (ii) lz(prefn(驴)) = O(1), and (iii) r(prefn(驴)) = lgn + O(1). De Bruijn words, well known for their high subword complexity are shown to have almost highest repetition complexity; the precise complexity remains open. r(w) can be computed in time O(n3(log n)2) and it is open, and probably very difficult, to find very fast algorithms.