An O(n log n) algorithm for finding all repetitions in a string
Journal of Algorithms
Theoretical Computer Science
Text algorithms
Repetitions in Sturmian strings
Theoretical Computer Science
Repetitive perhaps, but certainly not boring
Theoretical 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 structure of subword graphs and suffix trees of Fibonacci words
Theoretical Computer Science - Implementation and application of automata
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
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
How many runs can a string contain?
Theoretical Computer Science
Towards a Solution to the "Runs" Conjecture
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
The Number of Runs in Sturmian Words
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Language and Automata Theory and Applications
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Asymptotic behavior of the numbers of runs and microruns
Information and Computation
Repetitions in strings: Algorithms and combinatorics
Theoretical Computer Science
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
Hunting redundancies in strings
DLT'11 Proceedings of the 15th international conference on Developments in language theory
On primary and secondary repetitions in words
Theoretical Computer Science
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
On the maximum number of cubic subwords in a word
European Journal of Combinatorics
Computing the maximal-exponent repeats of an overlap-free string in linear time
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Computing maximum number of runs in strings
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
| Hi-index | 0.01 |
A run in a string is a nonextendable (with the same minimal period) periodic segment in a string. The set of runs corresponds to the structure of internal periodicities in a string. Periodicities in strings were extensively studied and are important both in theory and practice (combinatorics of words, pattern-matching, computational biology). Let ρ(n) be the maximal number of runs in a string of length n. It has been shown that ρ(n)=O(n), the proof was very complicated and the constant coefficient in O(n) has not been given explicitly. We demystify the proof of the linear upper bound for ρ(n) and propose a new approach to the analysis of runs based on the properties of subperiods:the periods of periodic parts of the runs We show that ρ(n)≤n and there are at most O.67n runs with periods larger than 87. This supports the conjecture that the number of all runs is smaller than n. We also give a completely new proof of the linear bound and discover several new interesting "periodicity lemmas".