TY - GEN
T1 - Faster and Simpler Online/Sliding Rightmost Lempel-Ziv Factorizations
AU - Sumiyoshi, Wataru
AU - Mieno, Takuya
AU - Inenaga, Shunsuke
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(nlogn) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(nlogn/loglogn)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms.
AB - We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(nlogn) time with O(n) space, due to Amir et al. [IPL 2002] for the online model, and due to Larsson [CPM 2014] for the sliding model. In this paper, we present faster O(nlogn/loglogn)-time solutions to both of the online/sliding models. Our algorithms are built on a simple data structure named BP-linked trees, and on a slightly improved version of the range minimum/maximum query (RmQ/RMQ) data structure on a dynamic list of integers. We also present other applications of our algorithms.
KW - closed factorizations
KW - Lempel-Ziv factorizations
KW - suffix trees
UR - http://www.scopus.com/inward/record.url?scp=85205382691&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85205382691&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-72200-4_24
DO - 10.1007/978-3-031-72200-4_24
M3 - Conference contribution
AN - SCOPUS:85205382691
SN - 9783031721991
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 321
EP - 335
BT - String Processing and Information Retrieval - 31st International Symposium, SPIRE 2024, Proceedings
A2 - Lipták, Zsuzsanna
A2 - Moura, Edleno
A2 - Figueroa, Karina
A2 - Baeza-Yates, Ricardo
PB - Springer Science and Business Media Deutschland GmbH
T2 - 31st International Symposium on String Processing and Information Retrieval, SPIRE 2024
Y2 - 23 September 2024 through 25 September 2024
ER -