Cover array string reconstruction
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2010Collection
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A proper fact or 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 C is the minimalcover (resp. maximalcover) array of y if C[i] is the minimal (resp. maximal) length of covers of y[0 ..i], or zero if no cover exists. In this paper, we present a constructive algorithm checking the validity of an array as a minimalcover or maximalcover 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 coverarrays: the sum of important values in a cover array is bounded by twice the length of the string.
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