Optimal in-place suffix sorting

• Main Authors: LI, Zhize, LI, Jian, HUO, Hongwei
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Suffix sorting; Suffix array; In-place; Databases and Information Systems
• Online Access: https://ink.library.smu.edu.sg/sis_research/8672; https://ink.library.smu.edu.sg/context/sis_research/article/9675/viewcontent/SPIRE18_suffixsort.pdf
• Institution: Singapore Management University

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 attentions and considerable advances have been made for the past 20 years. We obtain the first in-place linear time suffix array construction algorithms that are optimal both in time and space for (read-only) integer alphabets. Our 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 $|\Sigma| = O(n)$. Besides, we provide an optimal in-place $O(n \log n)$ time suffix sorting algorithm for read-only general alphabets (i.e., only comparisons are allowed), recovering the result obtained by Franceschini and Muthukrishnan which was an open problem posed by Manzini and Ferragina in ESA 2002.