Power laws and power-of-two-choices
Data Structures and Algorithms
2026-03-23 v1 Probability
Abstract
This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of randomly-chosen options is selected. We investigate what happens when the largest of randomly-chosen options is selected. This process generates a power-law-like distribution: the -smallest value scales with , where is the number of randomly-chosen options, with high probability. We give a formula for the expectation and show the distribution is concentrated around the expectation
Cite
@article{arxiv.2603.20060,
title = {Power laws and power-of-two-choices},
author = {Amanda Redlich},
journal= {arXiv preprint arXiv:2603.20060},
year = {2026}
}