Parallel Construction of Wavelet Trees on Multicore Architectures

TL;DR

This paper presents two parallel algorithms for constructing wavelet trees efficiently on multicore architectures, significantly reducing construction time and demonstrating practical speedups on large datasets.

Contribution

Introduces two novel parallel algorithms for wavelet tree construction leveraging multicore systems, improving speed and efficiency over existing methods.

Findings

First algorithm constructs all wavelet levels in parallel in O(n) time.

Second algorithm achieves O(log n) construction time using domain decomposition.

Both algorithms show good speedup on large real datasets.

Abstract

The wavelet tree has become a very useful data structure to efficiently represent and query large volumes of data in many different domains, from bioinformatics to geographic information systems. One problem with wavelet trees is their construction time. In this paper, we introduce two algorithms that reduce the time complexity of a wavelet tree's construction by taking advantage of nowadays ubiquitous multicore machines. Our first algorithm constructs all the levels of the wavelet in parallel in $O(n)$ time and $O(n\lg\sigma + \sigma\lg n)$ bits of working space, where $n$ is the size of the input sequence and $\sigma$ is the size of the alphabet. Our second algorithm constructs the wavelet tree in a domain-decomposition fashion, using our first algorithm in each segment, reaching $O(\lg n)$ time and $O(n\lg\sigma + p\sigma\lg n/\lg\sigma)$ bits of extra space, where $p$ is the number of available cores. Both algorithms are practical and report good speedup for large real datasets.