An Optimal Algorithm for Computing the Repetitions in a Word

@article{Crochemore1981AnOA,
title={An Optimal Algorithm for Computing the Repetitions in a Word},
author={Maxime Crochemore},
journal={Inf. Process. Lett.},
year={1981},
volume={12},
pages={244-250}
}
• M. Crochemore
• Published 13 October 1981
• Computer Science
• Inf. Process. Lett.
350 Citations
• Computer Science
CPM
• 2007
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.
The algorithm can be used to detect certain types of pseudo-patterns in words, which was the original goal in studying this generalization of Kosaraju's result.
• Mathematics
40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039)
• 1999
This work proves a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length n is bounded by a linear function in n, which implies that there is only a linear number of maximal repetition in a word.
• Computer Science
ICABD
• 2014
A new variant of Crochemore’s partitioning algorithm for weighted strings is presented, which requires optimal time O(n log n), thus improving on the best known O( n2)-time algorithm for computing all repetitions in a weighted string of length n.
• Computer Science
J. Autom. Lang. Comb.
• 2003
An algorithm that identifies all the repeating substrings (tandem, overlapping, and split) in a given string x = X[1..n] and its output substrings u are nonextendible (NE); that is, any extension of some occurrence of u in x, either to the left or to the right, yields a string (λu or uλ) that is unequal to the same Extension of some other occurrence of U.
• Computer Science
• 2010
This paper proposes a parallel approach to computing runs based on a parallelization of the extended Crochemore’s algorithm under the shared memory model.
• W. F. Smyth
• Computer Science
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2014
This paper explores the possibility that repetitions (perhaps also other regularities in strings) can be computed in a manner commensurate with the size of the output.
The approach introduced here for finding all valid models corresponding to either repeated or common motifs starts by building a suffix tree of the sequence(s) and then, after some further preprocessing, uses this tree to simply spell the models.
• Computer Science
Psychological science in the public interest : a journal of the American Psychological Society
• 2014
Three variants of extending the original Crochemore repetition algorithm to compute runs are presented – two with a worsen complexity of O(n log n), and one with the same complexity as the original algorithm.
• Computer Science
STACS
• 2015
It is shown that it is NP-complete to decide, for a given number k and a word w, whether w can be factorised into k distinct factors; this shows that the injective version of the matching problem isNP-complete even for very restricted cases.

References

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