Periods in partial words: an algorithm

Authors:
Francine Blanchet-Sadri;Travis Mandel;Gautam Sisodia
Affiliations:
Department of Computer Science, University of North Carolina, Greensboro, NC;Department of Mathematics, The University of Texas, Austin, TX;Department of Mathematics, University of Washington, Seattle, WA
Venue:
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Year:
2011

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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 $r = q \bmod{p}$. As a result, we give an algorithm for computing L(h, p, q) in the general case.