Abstract
A proper factor u of a string y is a cover of y if every letter of y is within some occurrence of u in y. The concept generalises the notion of periods of a string. An integer array \({\mathit{C}}\) is the minimal-cover (resp. maximal-cover) array of y if \({\mathit{C}}[i]\) is the minimal (resp. maximal) length of covers of \(y[0{\ldotp\ldotp}i]\), or zero if no cover exists.
In this paper, we present a constructive algorithm checking the validity of an array as a minimal-cover or maximal-cover array of some string. When the array is valid, the algorithm produces a string over an unbounded alphabet whose cover array is the input array. All algorithms run in linear time due to an interesting combinatorial property of cover arrays: the sum of important values in a cover array is bounded by twice the length of the string.
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Crochemore, M., Iliopoulos, C.S., Pissis, S.P., Tischler, G. (2010). Cover Array String Reconstruction. In: Amir, A., Parida, L. (eds) Combinatorial Pattern Matching. CPM 2010. Lecture Notes in Computer Science, vol 6129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13509-5_23
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DOI: https://doi.org/10.1007/978-3-642-13509-5_23
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