An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Theoretical Computer Science
Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Journal of the ACM (JACM)
How many squares can a string contain?
Journal of Combinatorial Theory Series A
The exact number of squares in Fibonacci words
Theoretical Computer Science
Repetitions in Sturmian strings
Theoretical Computer Science
Repetitive perhaps, but certainly not boring
Theoretical Computer Science
On Strongly Cube-Free Omega-Words Generated by Binary Morphisms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Computing all repeats using suffix arrays
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the 13th Australasian workshop on combinatorial algorithms
Linear time algorithms for finding and representing all the tandem repeats in a string
Journal of Computer and System Sciences
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
A simple proof that a word of length n has at most 2n distinct squares
Journal of Combinatorial Theory Series A
Algorithms on Strings
The structure of subword graphs and suffix trees of Fibonacci words
Theoretical Computer Science - Implementation and application of automata
A note on the number of squares in a word
Theoretical Computer Science
The number of runs in a string
Information and Computation
The Lempel-Ziv Complexity of Fixed Points of Morphisms
SIAM Journal on Discrete Mathematics
Computing Longest Previous Factor in linear time and applications
Information Processing Letters
Maximal repetitions in strings
Journal of Computer and System Sciences
How many runs can a string contain?
Theoretical Computer Science
A Simple Algorithm for Computing the Lempel Ziv Factorization
DCC '08 Proceedings of the Data Compression Conference
Fast and Practical Algorithms for Computing All the Runs in a String
CPM '07 Proceedings of the 18th annual symposium on Combinatorial Pattern Matching
The number of runs in a string: improved analysis of the linear upper bound
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Crochemore factorization of sturmian and other infinite words
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Analysis of maximal repetitions in strings
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Towards a Solution to the "Runs" Conjecture
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
A minimal periods algorithm with applications
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Extracting powers and periods in a string from its runs structure
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Theoretical Computer Science
On the maximal sum of exponents of runs in a string
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Unary pattern avoidance in partial words dense with holes
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
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
On the maximal sum of exponents of runs in a string
Journal of Discrete Algorithms
The maximal number of cubic runs in a word
Journal of Computer and System Sciences
New simple efficient algorithms computing powers and runs in strings
Discrete Applied Mathematics
Average number of occurrences of repetitions in a necklace
Discrete Applied Mathematics
Extracting powers and periods in a word from its runs structure
Theoretical Computer Science
Hi-index | 5.24 |
The article is an overview of basic issues related to repetitions in strings, concentrating on algorithmic and combinatorial aspects. This area is important both from theoretical and practical points of view. Repetitions are highly periodic factors (substrings) in strings and are related to periodicities, regularities, and compression. The repetitive structure of strings leads to higher compression rates, and conversely, some compression techniques are at the core of fast algorithms for detecting repetitions. There are several types of repetitions in strings: squares, cubes, and maximal repetitions also called runs. For these repetitions, we distinguish between the factors (sometimes qualified as distinct) and their occurrences (also called positioned factors). The combinatorics of repetitions is a very intricate area, full of open problems. For example we know that the number of (distinct) primitively-rooted squares in a string of length n is no more than 2n-@Q(logn), conjecture to be n, and that their number of occurrences can be @Q(nlogn). Similarly we know that there are at most 1.029n and at least 0.944n maximal repetitions and the conjecture is again that the exact bound is n. We know almost everything about the repetitions in Sturmian words, but despite the simplicity of these words, the results are nontrivial. One of the main motivations for writing this text is the development during the last couple of years of new techniques and results about repetitions. We report both the progress which has been achieved and which we expect to happen.