Bitvectors with runs and the successor/predecessor problem

The successor and predecessor problem consists of obtaining the closest value in a set of integers, greater/smaller than a given value. This problem has interesting applications, like the intersection of inverted lists. It can be easily modeled by using a bitvector of size $n$ and its operations rank and select. However, there is a practical approach, which keeps the best theoretical bounds, and allows to solve successor and predecessor more efficiently. Based on that technique, we designed a novel compact data structure for bitvectors with $k$ runs that achieves access, rank, and successor/predecessor in $O(1)$ time by consuming space $O(\sqrt{kn})$ bits. In practice, it obtains a compression ratio of $0.04\mathrm{\%}-26.33\mathrm{\%}$ when the runs are larger than $100$, and becomes the fastest technique, which considers compressibility, in successor/predecessor queries. Besides, we present a recursive variant of our structure, which tends to $O(k)$ bits and takes $O(\log \frac{n}{k})$ time.