Simple, Optimal Algorithms for Random Sampling Without Replacement

TL;DR

This paper introduces new simple and efficient algorithms for sampling without replacement from a finite set, improving on classical methods in simplicity and optimality.

Contribution

It presents novel algorithms that are simpler, easier to implement, and have optimal space and time complexity for sampling without replacement.

Findings

Algorithms are simpler and more practical than classical methods.

Achieves optimal space and time complexity.

Applicable to large-scale sampling problems.

Abstract

Consider the fundamental problem of drawing a simple random sample of size k without replacement from [n] := {1, . . . , n}. Although a number of classical algorithms exist for this problem, we construct algorithms that are even simpler, easier to implement, and have optimal space and time complexity.