Improved parallel construction of wavelet trees and rank/select structures

• Published in: Information and computation Vol. 273; no. C; p. 104516
• Main Author: Shun, Julian
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.08.2020; Elsevier
• Subjects: MATHEMATICS AND COMPUTING; Parallel algorithms; Rank and select; Succinct data structures; Wavelet matrix; Wavelet tree; Succinct data structures; Wavelet tree; Rank and select; Wavelet matrix; Parallel algorithms
• ISSN: 0890-5401; 1090-2651; 1090-2651
• DOI: 10.1016/j.ic.2020.104516

Existing parallel algorithms for wavelet tree construction have a work complexity of O(nlog⁡σ). This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer sorting and has either O(nlog⁡log⁡n⌈log⁡σ/log⁡nlog⁡log⁡n⌉) work and polylogarithmic depth, or O(n⌈log⁡σ/log⁡n⌉) work and sub-linear depth. We also describe another algorithm that has O(n⌈log⁡σ/log⁡n⌉) work and O(σ+log⁡n) depth. We then show how to use similar ideas to construct variants of wavelet trees (arbitrary-shaped binary trees and multiary trees) as well as wavelet matrices in parallel with lower work complexity than prior algorithms. Finally, we show that the rank and select structures on binary sequences and multiary sequences, which are stored on wavelet tree nodes, can be constructed in parallel with improved work bounds, matching those of the best existing sequential algorithms for constructing rank and select structures.