Practical Parallel Block Tree Construction

The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees. Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.