An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
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Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Text algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
How many squares can a string contain?
Journal of Combinatorial Theory Series A
The exact number of squares in Fibonacci words
Theoretical Computer Science
A Space-Economical Suffix Tree Construction Algorithm
Journal of the ACM (JACM)
Computation of Squares in a String (Preliminary Version)
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
Simple and Flexible Detection of Contiguous Repeats Using a Suffix Tree (Preliminary Version)
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
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Simple and flexible detection of contiguous repeats using a suffix tree
Theoretical Computer Science
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WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Repetition Complexity of Words
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Finding Approximate Repetitions under Hamming Distance
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
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Theoretical Computer Science - Logic and complexity in computer science
Speeding up the detection of evolutive tandem repeats
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Finding approximate tandem repeats in genomic sequences
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
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Journal of Discrete Algorithms - SPIRE 2002
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CSB '04 Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference
Linear-time computation of local periods
Theoretical Computer Science
Linear time algorithms for finding and representing all the tandem repeats in a string
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Theoretical Computer Science - Combinatorics on words
FireμSat: meeting the challenge of detecting microsatellites in DNA
SAICSIT '06 Proceedings of the 2006 annual research conference of the South African institute of computer scientists and information technologists on IT research in developing countries
The structure of subword graphs and suffix trees of Fibonacci words
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The number of runs in a string
Information and Computation
Computing Longest Previous Factor in linear time and applications
Information Processing Letters
Maximal repetitions in strings
Journal of Computer and System Sciences
Repetitions detection on a linear array with reconfigurable pipelined bus system
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Discovering regularities in biosequences: Challenges and applications
Journal of Computational Methods in Sciences and Engineering
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The Number of Runs in Sturmian Words
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Efficient on-line repetition detection
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LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
A fast algorithm for finding the positions of all squares in a run-length encoded string
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Abstractions in Process Mining: A Taxonomy of Patterns
BPM '09 Proceedings of the 7th International Conference on Business Process Management
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Efficient Algorithms for Two Extensions of LPF Table: The Power of Suffix Arrays
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
On the complexity of finding gapped motifs
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Testing square-freeness of strings compressed by balanced straight line program
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
A minimal periods algorithm with applications
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
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IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
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CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
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DLT'11 Proceedings of the 15th international conference on Developments in language theory
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WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
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STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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Journal of Discrete Algorithms
The lempel-ziv complexity of fixed points of morphisms
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
On the maximal number of cubic runs in a string
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
The structure of subword graphs and suffix trees of fibonacci words
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
On the maximal sum of exponents of runs in a string
Journal of Discrete Algorithms
Worst-case efficient single and multiple string matching on packed texts in the word-RAM model
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On suffix extensions in suffix trees
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MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
The maximal number of cubic runs in a word
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On the maximum number of cubic subwords in a word
European Journal of Combinatorics
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European Journal of Combinatorics
Computing the Longest Previous Factor
European Journal of Combinatorics
Fundamenta Informaticae
Analysis of maximal repetitions in strings
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Computing maximum number of runs in strings
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Effective periodic pattern mining in time series databases
Expert Systems with Applications: An International Journal
Fast algorithms for finding a minimum repetition representation of strings and trees
Discrete Applied Mathematics
Frequent patterns mining in multiple biological sequences
Computers in Biology and Medicine
A d-step approach to the maximum number of distinct squares and runs in strings
Discrete Applied Mathematics
Average number of occurrences of repetitions in a necklace
Discrete Applied Mathematics
Computing the number of cubic runs in standard Sturmian words
Discrete Applied Mathematics
Extracting powers and periods in a word from its runs structure
Theoretical Computer Science
Periodic pattern analysis of non-uniformly sampled stock market data
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A repetition in a word w is a sub-word with the period of at most half of the sub-word length. We study maximal repetitions occurring in w, that is those for which any extended sub-word of w has a bigger period. The set of such repetitions represents in a compact way all repetitions in w.We first prove 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. This implies, in particular, that there is only a linear number of maximal repetitions in a word. This allows us to construct a linear-time algorithm for finding all maximal repetitions. Some consequences and applications of these results are discussed, as well as related works.