Integer Representation and Counting in the Bit Probe Model

Abstract

We examine the problem of integer representation in near minimal number of bits so that increment and decrement (and indeed addition and subtraction) can be performed using few bit inspections and fewer bit changes. In particular, we prove a new lower bound of Ω(√n) for the increment and decrement operation, where n is the minimum number of bits required to represent the number. The model of computation we considered is the bit probe model, where the complexity measure counts only the bitwise accesses to the data structure. We present several efficient data structures to represent integer that use a logarithmic number of bit inspections and a constant number of bit changes per operation.