Simple Analysis of Priority Sampling

TL;DR

This paper provides a simplified and concise proof of a tight variance bound for the priority sampling method, resolving a longstanding conjecture in the field.

Contribution

It introduces a shorter, more accessible proof of the variance bound for priority sampling, improving understanding and potentially enabling further research.

Findings

Proved a tight upper bound on the variance of priority sampling

Simplified the proof significantly compared to previous work

Resolved a conjecture posed by Duffield, Lund, and Thorup

Abstract

We prove a tight upper bound on the variance of the priority sampling method (aka sequential Poisson sampling). Our proof is significantly shorter and simpler than the original proof given by Mario Szegedy at STOC 2006, which resolved a conjecture by Duffield, Lund, and Thorup.