Bannai, H. and Charalampopoulos, Panagiotis and Radoszewski, J. (2024) Maintaining the size of LZ77 on semi-dynamic strings. Leibniz International Proceedings in Informatics (LIPIcs) , ISSN 1868-8969.
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Abstract
We consider the problem of maintaining the size of the LZ77 factorization of a string S of length at most n under the following operations: (a) appending a given letter to S and (b) deleting the first letter of S. Our main result is an algorithm for this problem with amortized update time Õ(√n). As a corollary, we obtain an Õ(n√n)-time algorithm for computing the most LZ77-compressible rotation of a length-n string - a naive approach for this problem would compute the LZ77 factorization of each possible rotation and would thus take quadratic time in the worst case. We also show an Ω(√n) lower bound for the additive sensitivity of LZ77 with respect to the rotation operation. Our algorithm employs dynamic trees to maintain the longest-previous-factor array information and depends on periodicity-based arguments that bound the number of the required updates and enable their efficient computation.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Lempel-Ziv compression, LZ77, semi-dynamic algorithm, cyclic rotation |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Panagiotis Charalampopoulos |
| Date Deposited: | 15 Jul 2024 13:26 |
| Last Modified: | 11 Apr 2025 02:34 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/53512 |
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