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Bit vectors are fundamental building blocks of many succinct data structures.They can be used to represent graphs, are an important part of many textindices in the form of the wavelet tree, and can be used to encode orderedsequences of integers as Elias-Fano codes. To do so, two queries have to beanswered: namely rank and select queries. Given a position in the bit vector, arank query returns the number of 1-bits before that position. A select query,given a parameter $j$, returns the position of the $j$-th 1-bit. On a length-nbit vector, both queries can be answered in $O(1)$ time and require $o(n)$ bitsof additional space. In practice, the smallest (uncompressed) rank and selectdata structure cs-poppy has a space overhead of $\approx$ 3.51% [Zhou et al.,SEA 13]. In this paper, we present an improved rank and select data structurethat has the same space overhead but can answer queries up to 8% (rank) and16.5% (select) faster compared with cs-poppy.

Engineering Compact Data Structures for Rank and Select Queries on Bit Vectors