Algorithms for Generating Small Random Samples

TL;DR

This paper introduces efficient algorithms for generating small random samples without replacement, specifically for pairs and triples, with constant worst-case runtime, and provides open source Java implementations.

Contribution

It presents novel algorithms for small sample sizes with constant worst-case runtime, improving efficiency over general sampling methods.

Findings

Constant worst-case runtime for pair and triple sampling algorithms

Open source Java implementations included

Improved efficiency for small sample generation

Abstract

We present algorithms for generating small random samples without replacement. We consider two cases. We present an algorithm for sampling a pair of distinct integers, and an algorithm for sampling a triple of distinct integers. The worst-case runtime of both algorithms is constant, while the worst-case runtimes of common algorithms for the general case of sampling $k$ elements from a set of $n$ increase with $n$. Java implementations of both algorithms are included in the open source library $\rho\mu$.