Rank and Select for Succinct Data Structures

Abstract

In this paper, we study different approaches for rank and select on sequences of bytes and propose new implementation strategies. Extensive experimental evaluation comparing the efficiency of the different alternatives are provided. Given a sequence of bits, a rank query counts the number of occurrences of the bit 1 up to a given position, and a select query returns the position of the ith occurrence of the bit 1. These operations are widely used in information retrieval and management, being the base of several data structures and algorithms for text collections, graphs, etc. There exist solutions for computing these operations on sequences of bits in constant time using additional information. However, new applications require rank and select to be computed on sequences of bytes instead of bits. The solutions for the binary case are not directly applicable to sequences of bytes. The existing solutions for the byte case vary in their space-time trade-off which can still be improved.