Optimal in-place suffix sorting

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 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 |Σ|≤n. Our result is in fact slightly stronger since we allow |Σ|=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.