Fast Wavelet Tree Construction in Practice

Kaneta, Yusaku

doi:10.1007/978-3-030-00479-8_18

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…These approaches make use of vectorized instructions, i.e., SIMD (single instruction, multiple data), to achieve their running time. There also exist implementations that make use of vectorized instructions available in modern CPUs [24] and are reported to be the fastest in practice. In shared memory, wavelet trees can be computed in O(σ +log n) time requiring only O(n log σ/ √ log n) work [39].…”

Section: Preliminariesmentioning

confidence: 99%

Faster Wavelet Trees with Quad Vectors

Ceregini¹,

Kurpicz²,

Venturini³

2023

Preprint

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Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational geometry, and pattern matching in the form of the backwards search-the backbone of many compressed full-text indices. A wavelet tree is a compact data structure that for a text of length n over an alphabet of size σ requires only n log σ (1 + o( 1)) bits of space and can answer rank and select queries in Θ(log σ) time. Wavelet trees are used in the applications described above.In this paper, we show how to improve query performance of wavelet trees by using a 4-ary tree instead of a binary tree as basis of the wavelet tree. To this end, we present a space-efficient rank and select data structure for quad vectors. The 4-ary tree layout of a wavelet tree helps to halve the number of cache misses during queries and thus reduces the query latency. Our experimental evaluation shows that our 4-ary wavelet tree can improve the latency of rank and select queries by a factor of ≈ 2 compared to the wavelet tree implementations contained in the widely used Succinct Data Structure Library (SDSL). ACM Subject ClassificationTheory of computation → Data structures design and analysis; Applied computing → Document management and text processing; Applied computing → Document searching

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Section: Preliminariesmentioning

confidence: 99%

Faster Wavelet Trees with Quad Vectors

Ceregini¹,

Kurpicz²,

Venturini³

2023

Preprint

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“…We impose the restriction that for f −1 , the symbol c, for which a bit is being set in B M , has to be known when setting the bit. Even though this bit must ultimately have been computed from c, there are construction algorithms for the wavelet tree that redistribute the bits of c before constructing the bit vectors [1,7,9,11]. Due to the existence of our function f alone, such techniques may as well be used for the construction of the wavelet matrix.…”

Section: Translating Between Wavelet Tree and Matrix Constructionmentioning

confidence: 99%

Constructing the Wavelet Tree and Wavelet Matrix in Distributed Memory

Dinklage

Fischer

Kurpicz

2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

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The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 2015]) are compact data structures with many applications such as text indexing or computational geometry. By continuing the recent research of Fischer et al. [ALENEX, 2018], we explore the similarities and differences of these heavily related data structures with focus on their construction. We develop a data structure to modify construction algorithms for either the wavelet tree or matrix to construct instead the other. This modification is efficient, in that it does not worsen the asymptotic time and space requirements of any known wavelet tree or wavelet matrix construction algorithm.

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“…First, Fischer et al [5] introduced bottom-up wavelet construction algorithms that are very fast and memory efficient in practice, and result in the fastest sequential and shared memory parallel wavelet tree and matrix construction algorithms. Also, Kaneta [11] recently presented a practical implementation of the O n lg σ/ √ lg n -construction time algorithm, which uses word packing techniques in word-RAM, and has been (independently) introduced by Babenko et al [2] and Munro et al [16].…”

Section: Introductionmentioning

confidence: 99%