Publication Type
Journal Article
Version
publishedVersion
Publication Date
5-2022
Abstract
The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and considerable advances have been made for the past 20 years. We obtain the \emph{first} in-place suffix array construction algorithms that are optimal both in time and space for (read-only) integer alphabets. Concretely, we make the following contributions: 1. For integer alphabets, we obtain the first suffix sorting algorithm which takes linear time and uses only $O(1)$ workspace (the workspace is the total space needed beyond the input string and the output suffix array). The input string may be modified during the execution of the algorithm, but should be restored upon termination of the algorithm. 2. We strengthen the first result by providing the first in-place linear time algorithm for read-only integer alphabets with $|\Sigma|=O(n)$ (i.e., the input string cannot be modified). This algorithm settles the open problem posed by Franceschini and Muthukrishnan in ICALP 2007. The open problem asked to design in-place algorithms in $o(n\log n)$ time and ultimately, in $O(n)$ time for (read-only) integer alphabets with $|\Sigma| \leq n$. Our result is in fact slightly stronger since we allow $|\Sigma|=O(n)$. 3. Besides, for the read-only general alphabets (i.e., only comparisons are allowed), we present an optimal in-place $O(n\log n)$ time suffix sorting algorithm, recovering the result obtained by Franceschini and Muthukrishnan which was an open problem posed by Manzini and Ferragina in ESA 2002.
Keywords
Suffix sorting, Suffix array, In-place, Optimal time
Discipline
Databases and Information Systems
Research Areas
Data Science and Engineering; Intelligent Systems and Optimization
Publication
Information and Computation
Volume
285
First Page
1
Last Page
25
ISSN
0890-5401
Identifier
10.1016/j.ic.2021.104818
Publisher
Elsevier
Citation
LI, Zhize; LI, Jian; and HUO, Hongwei.
Optimal in‐place suffix sorting. (2022). Information and Computation. 285, 1-25.
Available at: https://ink.library.smu.edu.sg/sis_research/8690
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.ic.2021.104818