Finding Maximal Repetitions in a Word in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The number of runs in a string
Information and Computation
How many runs can a string contain?
Theoretical Computer Science
Language and Automata Theory and Applications
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
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
Analysis of maximal repetitions in strings
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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A run (also called maximal repetition) in a word is a non-extendable repetition. Finding the maximum number ρ(n) of runs in a string of length n is a challenging problem. Although it is known that ρ(n)≤1.029n for any n and there exists large n such that ρ(n)≥0.945n, the exact value of ρ(n) is still unknown. Several algorithms have been proposed to count runs in a string efficiently, and ρ(n) can be obtained for small n by these algorithms. In this paper, we focus on computing ρ(n) for given length parameter n, instead of exhaustively counting all runs for every string of length n. We report exact values of ρ(n) for binary strings for n≤66, together with the strings which contain ρ(n) runs.