Constructing suffix arrays in linear time

Abstract

The time complexity of suffix tree construction has been shown to be equivalent to that of sorting: O(n) for a constant-size alphabet or an integer alphabet and O(n log n) for a general alphabet. However, previous algorithms for constructing suffix arrays have the time complexity of O(n log n) even for a constant-size alphabet.In this paper we present a linear-time algorithm to construct suffix arrays for integer alphabets, which do not use suffix trees as intermediate data structures during its construction. Since the case of a constant-size alphabet can be subsumed in that of an integer alphabet, our result implies that the time complexity of directly constructing suffix arrays matches that of constructing suffix trees.

Computing Longest Previous Factor in linear time and applications

“…The algorithm Compute LPF uses O(n) space. Using the fact that the suffix array of a string of length n over an integer alphabet can be computed in O(n) time by any of the algorithms in [7,9,11,12], we obtain: Theorem 1. Given a string of length n over an integer alphabet, the LPF and PrevOcc arrays can be computed in time and space O(n).…”

Indexing a sequence for mapping reads with a single mismatch

“…Suffix arrays were first introduced in [46], where an O(n log n) construction algorithm and O(m + log n + |Occ T P |) query time were presented. Later, linear time construction algorithms for space efficient suffix arrays were presented [8,9,47,48]. The query time is also improved to optimal O(m + |Occ T P |) in [49] with the help of another array essentially storing the lengths of the longest common prefixes between lexicographically consecutive suffixes.…”

“…Finally, we note that there are several linear time suffix array construction methods that work with integer alphabet as well (e.g. [9,47]). …”

Efficient indexing algorithms for one-dimensional discretely-scaled strings

“…Given a text T over the alphabet Σ , the suffix tree [9,14] [10]. The details for suffix trees and suffix arrays are omitted here, since they are beyond the scope of this paper.…”

“…When both P and T are onedimensional strings, the problem is also called string matching, which can be solved in linear time [11]. Similar to but different from string matching, the string indexing problem aims to preprocess T , so that P can be detected more efficiently [10,14]. Recently, related problems that involve matching [2][3][4][5] or indexing [12,13,15] scaled strings have drawn much attention, because they are considered realistic in the field of computer vision.…”