Periods in partial words: An algorithm

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Abstract

Partial words are finite sequences over a finite alphabet that may contain some holes. A variant of the celebrated Fine-Wilf theorem shows the existence of a bound L = L(h,p,q) such that if a partial word of length at least L with h holes has periods p and q, then it has period gcd(p,q). In this paper, we associate a graph with each p- and q-periodic word, and study two types of vertex connectivity on such a graph: modified degree connectivity and r-set connectivity where r = q mod p. As a result, we give an algorithm for computing L(h, p, q) in the general case. © 2011 Springer-Verlag.

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Blanchet-Sadri, F., Mandel, T., & Sisodia, G. (2011). Periods in partial words: An algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7056 LNCS, pp. 57–70). https://doi.org/10.1007/978-3-642-25011-8_5

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