Shortest cover after edit
CoRR(2024)
摘要
This paper investigates the (quasi-)periodicity of a string when the string
is edited. A string C is called a cover (as known as a quasi-period) of a
string T if each character of T lies within some occurrence of C. By
definition, a cover of T must be a border of T; that is, it occurs both as
a prefix and as a suffix of T. In this paper, we focus on the changes in the
longest border and the shortest cover of a string when the string is edited
only once. We propose a data structure of size O(n) that computes the longest
border and the shortest cover of the string in O(ℓ + log n) time after an
edit operation (either insertion, deletion, or substitution of some string) is
applied to the input string T of length n, where ℓ is the length of
the string being inserted or substituted. The data structure can be constructed
in O(n) time given string T.
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