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Algorithms for Computing the [lambda]-regularities in Strings

Zhang H., Guo Q., Iliopoulos C.S.

Fundamenta Informaticae

2008

Vol. 84, nr 1

33-49

We introduce the notion of [lambda]-regularities in strings that consist of [lambda]-covers and [lambda]-seeds, and study three [lambda]-regularities problems- the [lambda]-cover problem, the general [lambda]-cover problem and the [lambda]-seed problem in this paper. [lambda]-regularities can be viewed as generalized string regularities in the sense that a set of [lambda] repetitive strings rather than a single repeated string are considered. We first present a general algorithm for computing all the [lambda]-combinations of a given string, since they serve as candidates for both [lambda]-covers and [lambda]-seeds. The running time of this algorithm is O(n2). Relying on this result, we answer the above mentioned three problems all in O(n2) time.