Online and Offline Algorithms for Counting Distinct Closed Factors via Sliding Suffix Trees
<|reference_start|>Online and Offline Algorithms for Counting Distinct Closed Factors via Sliding Suffix Trees: 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.<|reference_end|>
@article{mieno2024online,
    title={Online and Offline Algorithms for Counting Distinct Closed Factors via
  Sliding Suffix Trees},
    author={Takuya Mieno, Shun Takahashi, Kazuhisa Seto, and Takashi Horiyama},
    journal={arXiv preprint arXiv:2409.19576},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.19576},
    primaryClass={cs.DS}
}