Algorithms for Generating Small Random Samples

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 $\rho \mu$.