Linear work suffix array construction

Abstract

Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear-time construction algorithms and more explicit structure. We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays. The simplicity is demonstrated with a C++ implementation of 50 effective lines of code. The algorithm is called DC3, which stems from the central underlying concept of difference cover . This view leads to a generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space--time tradeoff. For any v ∈ [1, √n ], it runs in O( vn ) time using O( n / √v ) space in addition to the input string and the suffix array. We also present variants of the algorithm for several parallel and hierarchical memory models of computation. The algorithms for BSP and EREW-PRAM models are asymptotically faster than all previous suffix tree or array construction algorithms.

Bounded Prefix-Suffix Duplication

“…These words are assumed to be over an integer alphabet; that is, if w is the input word, and has length n, then we assume that its letters are integers from the set {l,...,n}. See a discussion about this assumption in [9]. If the input to our problems is a language, then we assume that this language is specified by a procedure deciding it (e.g., if the language is regular, trien we assume that we are given a DFA accepting it).…”

“…For details, see, e.g., [8,9]. Similarly, one can construct in linear time data structures allowing us to retrieve in constant time the length of the longest common suffix of any two prefixes w[l..¿] and w[l..j] of u, denoted LCS(i,j).…”

Binary block order Rouen Transform

“…To sort the rotations of a binary string into a BWT matrix in B-order, we will apply a linear-time suffix-sorting algorithm, such as that of Kärkkäinen and Sanders [KS03], Kärkkäinen, Sanders and Burkhardt [KSB06], Ko and Aluru [KA03], or Nong, Zhang, and Chan [NZC09].…”

Large-scale methods in computational genomics

“…In the first step, construct a suffix array (denoted by SA) data structure [Manber and Myers (1993)] on s in linear time [Karkkanen and Sander (2003) Maintaining the sorted order is critical for efficient generation of candidate pairs, as will soon become evident.…”

“…For the preprocessing phase, the construction of suffix array [Karkkanen and Sander (2003); Lemma 4, the cost of Step S3 over all iterations is proportional to the number of candidate pairs generated. For steps Si and S%, note that at worst case, locating a particular bi may take O(n) if it is the first entry in its Lset.…”