Internal shortest absent word queries in constant time and linear space

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. We present an O(n)-space data structure that answers such queries in...

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Bibliographic Details
Published in:Theoretical computer science Vol. 922; pp. 271 - 282
Main Authors: Badkobeh, Golnaz, Charalampopoulos, Panagiotis, Kosolobov, Dmitry, Pissis, Solon P.
Format: Journal Article
Language:English
Published: Elsevier B.V 24.06.2022
Subjects:
Bit parallelism
Internal queries
Shortest absent word
String algorithms
String algorithms
Bit parallelism
Shortest absent word
Internal queries
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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. We present an O(n)-space data structure that answers such queries in constant time and can be constructed in O(nlogσ⁡n) time.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.04.029