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 \(r = q \bmod{p}\). As a result, we give an algorithm for computing L(h, p, q) in the general case.
This material is based upon work supported by the National Science Foundation under Grant No. DMS–0452020.
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Blanchet-Sadri, F., Mandel, T., Sisodia, G. (2011). Periods in Partial Words: An Algorithm. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_5
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DOI: https://doi.org/10.1007/978-3-642-25011-8_5
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