Rank and select: Another lesson learned

TL;DR

This paper introduces new rank and select algorithms optimized for compressed bitmaps, demonstrating that tailored solutions and efficient handling of special cases improve performance without significant space overhead.

Contribution

It presents novel rank/select variants focusing on speed, showing that no single solution fits all data types and that optimized handling of uniform blocks enhances efficiency.

Findings

No single rank/select solution is best for all data types

Efficient handling of all-zero or all-one blocks improves performance

Compressed select can be nearly as fast as compressed rank with similar memory use

Abstract

Rank and select queries on bitmaps are essential building bricks of many compressed data structures, including text indexes, membership and range supporting spatial data structures, compressed graphs, and more. Theoretically considered yet in 1980s, these primitives have also been a subject of vivid research concerning their practical incarnations in the last decade. We present a few novel rank/select variants, focusing mostly on speed, obtaining competitive space-time results in the compressed setting. Our findings can be summarized as follows: $(i)$ no single rank/select solution works best on any kind of data (ours are optimized for concatenated bit arrays obtained from wavelet trees for real text datasets), $(ii)$ it pays to efficiently handle blocks consisting of all 0 or all 1 bits, $(iii)$ compressed select does not have to be significantly slower than compressed rank at a comparable memory use.