Space Efficient Construction of Lyndon Arrays in Linear Time

Bille, Philip; Ellert, Jonas; Fischer, Johannes; Gørtz, Inge Li; Kurpicz, Florian; Munro, J. Ian; Rotenberg, Eva

doi:10.4230/lipics.icalp.2020.14

Cited by 2 publications

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“…R ← R ∪ {⟨i, j, p⟩} Time and space complexity. The NSS array can be computed in O(n) time and space for general ordered alphabets [3]. Assume for now that we can answer L-LCE and R-LCE queries in constant time, then clearly the rest of the algorithm also requires O(n) time and space.…”

Section: Preliminariesmentioning

confidence: 99%

Linear Time Runs over General Ordered Alphabets

Ellert,

Fischer

2021

Preprint

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A run in a string is a maximal periodic substring. For example, the string bananatree contains the runs anana = (an) 3/2 and ee = e 2 . There are less than n runs in any length-n string, and computing all runs for a string over a linearly-sortable alphabet takes O(n) time (Bannai et al., SODA 2015). Kosolobov conjectured that there also exists a linear time runs algorithm for general ordered alphabets (Inf. Process. Lett. 2016). The conjecture was almost proven by Crochemore et al., who presented an O(nα(n)) time algorithm (where α(n) is the extremely slowly growing inverse Ackermann function). We show how to achieve O(n) time by exploiting combinatorial properties of the Lyndon array, thus proving Kosolobov's conjecture. ACM Subject Classification Theory of computation → Design and analysis of algorithmsKeywords and phrases String algorithms, Lyndon array, runs, longest common extension, general ordered alphabets, combinatorics on words Supplementary Material https://github.com/jonas-ellert/linear-time-runs/

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Section: Preliminariesmentioning

confidence: 99%

Linear Time Runs over General Ordered Alphabets

Ellert,

Fischer

2021

Preprint

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Generic Non-recursive Suffix Array Construction

Olbrich,

Ohlebusch,

Büchler

2024

ACM Trans. Algorithms

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The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive linear-time suffix array construction algorithm (SACA). Despite its interesting theoretical properties, there has been little effort in improving GSACA ’s non-competitive real-world performance. There is a super-linear algorithm DSH which relies on the same sorting principle and is faster than DivSufSort , the fastest SACA for over a decade. The purpose of this paper is twofold: We analyse the sorting principle used in GSACA and DSH and exploit its properties in order to give an optimised linear-time algorithm, and we show that it can be very elegantly used to compute both the original extended Burrows-Wheeler transform ( \(\mathsf {eBWT} \) ) and a bijective version of the Burrows-Wheeler transform ( \(\mathsf {BBWT} \) ) in linear time. We call the algorithm “generic” since it can be used to compute the regular suffix array and the variants used for the \(\mathsf {BBWT} \) and \(\mathsf {eBWT} \) . Our suffix array construction algorithm is not only significantly faster than GSACA but also outperforms DivSufSort and DSH . Our \(\mathsf {BBWT} \) -algorithm is faster than or competitive with all other tested \(\mathsf {BBWT} \) construction implementations on large or repetitive data, and our \(\mathsf {eBWT} \) -algorithm is faster than all other programs on data that is not extremely repetitive.

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Space Efficient Construction of Lyndon Arrays in Linear Time

Cited by 2 publications

References 0 publications

Linear Time Runs over General Ordered Alphabets

Linear Time Runs over General Ordered Alphabets

Generic Non-recursive Suffix Array Construction

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