Periodicity and repetitions in parameterized strings
نویسندگان
چکیده
منابع مشابه
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...
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A weak repetition in a string consists of two or more adjacent substrings which are permutations of each other. We describe a straightforward (n 2) algorithm which computes all the weak repetitions in a given string of length n deened on an arbitrary alphabet A. Using results on Fibonacci and other simple strings, we prove that this algorithm is asymptotically optimal over all known encodings o...
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In a recent paper we introduced infinite two-pattern strings on the alphabet {a, b} as a generalization of Sturmian strings, and we posed three questions about them: • Given a finite string x, can we in linear time O(|x|) recognize whether or not x is a prefix/substring of some infinite two-pattern string? • If recognized as two-pattern, can all the repetitions in x be computed in linear time? ...
متن کاملUnderstanding 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.
متن کاملApproximate Periodicity in Strings
In many application areas (for instance, DNA sequence analysis), it becomes important to compute various kinds of \approximate period" of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y ii y is a concatenation of substrings which are p...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2008
ISSN: 0166-218X
DOI: 10.1016/j.dam.2006.11.017