On estimating the alphabet size of a discrete random source

TL;DR

This paper introduces a memory-efficient algorithm to estimate the size of a discrete alphabet from a random symbol stream, achieving sublinear complexity in both time and space.

Contribution

It proposes a novel memory-restricted variant of an existing algorithm that estimates alphabet size with $O(\sqrt{N})$ complexity.

Findings

Estimates alphabet size in $O(\sqrt{N})$ time and space.

Provides analysis of the memory-restricted algorithm's performance.

Demonstrates effectiveness of the approach for large alphabet sizes.

Abstract

We are concerned with estimating alphabet size $N$ from a stream of symbols taken uniformly at random from that alphabet. We define and analyze a memory-restricted variant of an algorithm that have been earlier proposed for this purpose. The alphabet size $N$ can be estimated in $O(\sqrt{N})$ time and space by the memory-restricted variant of this algorithm.