Rank-Select Indices Without Tears

A rank-select index for a sequence B = (b1, . . . , bn) of n bits, where n ∈ N = {1, 2, . . .}, is a data structure that, if provided with an operation to access Θ(log n) arbitrary consecutive bits of B in constant time (thus B is stored outside of the data structure), can compute rankB(j) = ∑j i=1 bi for given j ∈ {0, . . . , n} and selectB(k) = min{j ∈ N | rankB(j) ≥ k} for given k ∈ {1, . . . , ∑n i=1 bi}. We describe a new rank-select index that, like previous rank-select indices, occupies O(n log log n/log n) bits and executes rank and select queries in constant time. Its derivation is intended to be particularly easy to follow and largely free of tedious low-level detail, its operations are given by straight-line code, and we show that it can be constructed in O(n/log n) time.