Online and Offline Algorithms for Counting Distinct Closed Factors via Sliding Suffix Trees
Abstract
A string is said to be closed if its length is one, or if it has a non-empty factor that occurs both as a prefix and as a suffix of the string, but does not occur elsewhere. The notion of closed words was introduced by [Fici, WORDS 2011]. Recently, the maximum number of distinct closed factors occurring in a string was investigated by [Parshina and Puzynina, Theor. Comput. Sci. 2024], and an asymptotic tight bound was proved. In this paper, we propose two algorithms to count the distinct closed factors in a string T of length n over an alphabet of size \sigma. The first algorithm runs in O(n log \sigma) time using O(n) space for string T given in an online manner. The second algorithm runs in O(n) time using O(n) space for string T given in an offline manner. Both algorithms utilize suffix trees for sliding windows.
Keywords
Cite
@article{arxiv.2409.19576,
title = {Online and Offline Algorithms for Counting Distinct Closed Factors via Sliding Suffix Trees},
author = {Takuya Mieno and Shun Takahashi and Kazuhisa Seto and Takashi Horiyama},
journal= {arXiv preprint arXiv:2409.19576},
year = {2024}
}