Engineering Rank/Select Data Structures for Large-Alphabet Strings

• Main Authors: Arroyuelo, Diego, Carmona, Gabriel, Larrañaga, Héctor, Riveros, Francisco, Rojas-Morales, Carlos Eugenio, Sepúlveda, Erick
• Format: Journal Article
• Language: English
• Published: 23.05.2023
• Subjects: Computer Science - Data Structures and Algorithms
• DOI: 10.48550/arxiv.2305.14461

Large-alphabet strings are common in scenarios such as information retrieval and natural-language processing. The efficient storage and processing of such strings usually introduces several challenges that are not witnessed in small-alphabets strings. This paper studies the efficient implementation of one of the most effective approaches for dealing with large-alphabet strings, namely the \emph{alphabet-partitioning} approach. The main contribution is a compressed data structure that supports the fundamental operations $rank$ and $select$ efficiently. We show experimental results that indicate that our implementation outperforms the current realizations of the alphabet-partitioning approach. In particular, the time for operation $select$ can be improved by about 80%, using only 11% more space than current alphabet-partitioning schemes. We also show the impact of our data structure on several applications, like the intersection of inverted lists (where improvements of up to 60% are achieved, using only 2% of extra space), the representation of run-length compressed strings, and the distributed-computation processing of $rank$ and $select$ operations. In the particular case of run-length compressed strings, our experiments on the Burrows-Wheeler transform of highly-repetitive texts indicate that by using only about 0.98--1.09 times the space of state-of-the-art RLFM-indexes (depending on the text), the process of counting the number of occurrences of a pattern in a text can be carried out 1.23--2.33 times faster.