Optimal in-place suffix sorting

Abstract

The suffix array is a fundamental data structure for many applications that involve string searching and data compression. We obtain the first in-place suffix array construction algorithms that are optimal both in time and space for (read-only) integer alphabets. We make the following contributions:1.For integer alphabets, we obtain the first linear time suffix sorting algorithm which uses only O(1) workspace. 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 |Σ|=O(n) (i.e., the input string cannot be modified). This algorithm settles the open problem posed by Franceschini and Muthukrishnan in ICALP 2007.3.Besides, for the read-only general alphabets (i.e., only comparisons are allowed), we present an optimal in-place O(nlog⁡n) time suffix sorting algorithm.