Improved parallel construction of wavelet trees and rank/select structures
Name
1610.03524.pdf
Description
Accepted version
Size
691.05 KB
Format
Adobe PDF
Checksum (MD5)
97d90d9e52770474d0be2b16b94ffc11
Author(s)
Shun, Julian
Date Issued
August 2020
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.IC.2020.104516
