Two-dimensional maximal repetitions

Maximal repetitions in strings

The cornerstone of any algorithm computing all repetitions in strings of length n in O(n) time is the fact that the number of maximal repetitions (runs) is linear. Therefore, the most important part of the analysis of the running time of such algorithms is counting the number of runs. Kolpakov and Kucherov [FOCS’99] proved it to be cn but could not provide any value for c. Recently, Rytter [STA...

On Maximal Repetitions in Words

Understanding Maximal Repetitions in Strings

The cornerstone of any algorithm computing all repetitions in a string of length n in O(n) time is the fact that the number of runs (or maximal repetitions) is O(n). We give a simple proof of this result. As a consequence of our approach, the stronger result concerning the linearity of the sum of exponents of all runs follows easily.

Two-dimensional interleaving schemes with repetitions: Constructions and bounds

Two-dimensional interleaving schemes with repetitions are considered. These schemes are required for the correction of two-dimensional bursts (or clusters) of errors in applications such as optical recording and holographic storage. We assume that a cluster of errors may have an arbitrary shape, and is characterized solely by its area . Thus, an interleaving scheme ( ) of strength with repetiti...

Maximal repetitions and Application to DNA sequences

In this paper we describe an implementation of Main-Kolpakov-Kucherov algorithm [9] of linear-time search for maximal repetitions in sequences. We first present a theoretical background and sketch main components of the method. We also discuss how the method can be generalized to finding approximate repetitions. Then we discuss implementation decisions and present test examples of running the p...