Given a string T of length n over an alphabet Σ ⊂ {1, 2, . . . , nO(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. For any positive integer k ∈ [1, log logσ n], we present an O((n/k) · log logσ n)-size data structure, which can be constructed in O(n logσ n) time, and answers queries in time O(log logσ k).

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doi.org/10.4230/LIPIcs.CPM.2021.6
Leibniz International Proceedings in Informatics
CPM 2021 - 32nd Annual Symposium on Combinatorial Pattern Matching
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Badkobeh, G, Charalampopoulos, P, & Pissis, S. (2021). Internal shortest absent word queries. In Proceedings of the 32nd Annual Symposium on Combinatorial Pattern Matching CPM 2021 (pp. 6:1–6:18). doi:10.4230/LIPIcs.CPM.2021.6