Rank-select indices without tears

Abstract

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 a constant-time operation to access (the integer whose binary representation is) the subsequence of B in Θ(log n) specified consecutive positions (thus B is stored outside of the data structure), can compute rank (formula presented) for given j∈ { 0, …, n} and select (formula presented) for given (formula presented). We describe a new rank-select index that, like previous rank-select indices, occupies O(nlog log n/log n) bits and executes rank and select queries in constant time. Its derivation is intended to be largely free of tedious low-level detail, its operations are given by straight-line code, and it can be constructed in O(n/log n) time if B can be accessed as above.