Linear-Time Construction of Suffix Arrays

Abstract

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.

Analyzing very large time series using suffix arrays

“…So far the main efforts of researchers who used suffix arrays and trees have focused on the optimization of the construction time [28][29][30] and more specifically on constructing the structure with linear time complexity [15,29]. Especially for suffix arrays the construction complexity depends on the sorting process [15,31].…”

“…Especially for suffix arrays the construction complexity depends on the sorting process [15,31]. Many techniques have been introduced that focus on the Longest Common Prefix (LCP) [14,15,29], denoted lcp(a, b), which is the longest common prefix between strings a and b.…”

String Data Structures for Computational Molecular Biology

“…This procedure takes linear time but cancels the main advantage of the suffix tree, which is the small space consumption. In 2003, three papers were published [58,75,26] that describe a worst-case linear time construction of a suffix array without the need of an initial construction of the respective suffix tree. Other algorithms for constructing suffix arrays can be found in [17,36,47,55,68].…”

LPF Computation Revisited

“…Introduced by Manber and Myers [16] the structure can be built in linear-time by different methods [10,12,13,8] for sorting the suffixes of the text possibly adding the method of [11] to compute the Longest Common Prefix table. The result holds if the text is drawn from an integer alphabet, that is, if the alphabet of the text can be sorted in linear time (otherwise the Ω(n log n) lower bound for sorting applies).…”

“…The computation of the Suffix Array of y can be done in time O(n log n) in the comparison model [16] (see [3,6,9]). If the text is on an alphabet of integers in the range [0, n c ] for some constant c, the Suffix Array can be built in time O(n) [10,12,13,8] (see also [3]). …”