Improved parallel construction of wavelet trees and rank/select structures
Author(s)
Shun, Julian
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Existing parallel algorithms for wavelet tree construction have a work complexity of O(nlogσ). 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(nloglogn⌈logσ/lognloglogn⌉) work and polylogarithmic depth, or O(n⌈logσ/logn⌉) work and sub-linear depth. We also describe another algorithm that has O(n⌈logσ/logn⌉) work and O(σ+logn) 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.
Date issued
2020-08Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence LaboratoryJournal
Information and Computation
Publisher
Elsevier BV
Citation
Shun, Julian. “Improved parallel construction of wavelet trees and rank/select structures.” Information and Computation, 273 (August 2020): 104516 © 2020 The Author
Version: Author's final manuscript
ISSN
0890-5401