The article investigates the changes in the shortest cover of a string when the string is edited. It focuses on two problems: the LBAE (Longest Border After-Edit) query and the SCAE (Shortest Cover After-Edit) query.
For the LBAE query, the article proposes an O(n)-size data structure that can compute the longest border of the edited string in O(ℓ + log n) time, where ℓ is the length of the inserted or substituted string.
For the SCAE query, the article first solves the LBAE query to obtain the border of the edited string. It then considers two cases: the non-periodic case, where the border is shorter than half the length of the edited string, and the periodic case.
In the non-periodic case, the article shows how to determine whether the cover of the border can cover the entire edited string. If not, it groups the borders of the prefix of the edited string by their periods and processes each group to find a border that can be extended to cover the entire edited string.
In the periodic case, the article exploits the periodic structure of the edited string to efficiently compute its shortest cover.
Overall, the article presents efficient algorithms to compute the shortest cover of a string after an edit operation, using a combination of data structures and combinatorial properties of borders and covers.
To Another Language
from source content
arxiv.org
Djupare frågor