History-Independent Load Balancing

TL;DR

This paper introduces a history-independent load balancing algorithm for dynamic balls-and-bins problems that guarantees near-optimal maximum load with low expected recourse, advancing the state of fully dynamic load balancing solutions.

Contribution

It presents the first history-independent algorithm with nontrivial guarantees for large load ratios and the first fully dynamic solution achieving constant overload with sublinear expected recourse.

Findings

Achieves maximum load of m/n + O(1) with high probability

Expected recourse per operation is O(log log(m/n))

First fully dynamic solution with O(1) overload and o(m/n) recourse

Abstract

We give a (strongly) history-independent two-choice balls-and-bins algorithm on $n$ bins that supports both insertions and deletions on a set of up to $m$ balls, while guaranteeing a maximum load of $m / n + O(1)$ with high probability, and achieving an expected recourse of $O(\log \log (m/n))$ per operation. To the best of our knowledge, this is the first history-independent solution to achieve nontrivial guarantees of any sort for $m/n \ge \omega(1)$ and is the first fully dynamic solution (history independent or not) to achieve $O(1)$ overload with $o(m/n)$ expected recourse.