Internal Shortest Absent Word Queries in Constant Time and Linear Space

Abstract

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 fragmentWe present an O(n)-space data structure that answers such queries in constant time and can be constructed in O(n log σ n) time.