Rank/Select Queries over Mutable Bitmaps

TL;DR

This paper introduces a practical method for efficiently performing rank/select queries on mutable bitmaps, allowing bit modifications with minimal performance impact and lower space usage compared to existing immutable solutions.

Contribution

It extends prefix-sum data structures to support mutable bitmaps with efficient updates, improving runtime and space efficiency over prior methods.

Findings

Improved runtime performance over state-of-the-art solutions.

No significant space overhead introduced by the new method.

Supports fast flip operations with minimal impact on query speed.

Abstract

The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the case where one is allowed to modify the bitmap via a flip(i) operation that toggles its i-th bit. By adapting and properly extending some results concerning prefix-sum data structures, we present a practical solution to the problem, tailored for modern CPU instruction sets. Compared to the state-of-the-art, our solution improves runtime with no space degradation. Moreover, it does not incur in a significant runtime penalty when compared to the fastest immutable indexes, while providing even lower space overhead.