Internal Shortest Absent Word Queries in Constant Time and Linear Space

06/03/2021

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by   Golnaz Badkobeh, et al.

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Given a string T of length n over an alphabet Σ⊂{1,2,…,n^O(1)} of size σ, we are to preprocess T so that given a range [i,j], we can return a representation of a shortest string over Σ that is absent in the fragment T[i]⋯ T[j] of T. We present an O(n)-space data structure that answers such queries in constant time and can be constructed in O(nlog_σ n) time.