History-Independent Load Balancing

2026-02-12

AI Summary

This work addresses the challenge of simultaneously achieving load balancing, strong history independence, and low adjustment cost in fully dynamic settings supporting arbitrary insertions and deletions. We present the first strongly history-independent “two-choice” balls-into-bins algorithm that dynamically manages up to $m$ balls across $n$ bins, where $m/n = \omega(1)$. With high probability, the maximum load is bounded by $m/n + O(1)$, and the expected adjustment cost per operation is only $O(\log\log(m/n))$. Our scheme is the first to achieve non-trivial history-independent load balancing under the condition $m/n = \omega(1)$, while simultaneously guaranteeing $O(1)$ overload and an expected adjustment cost of $o(m/n)$.

Technology Category

• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design
• Search and Optimization: Algorithm Configuration

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• load balancing
• balls-and-bins
• history independence
• dynamic operations
• maximum load

Innovation

• history-independent
• load balancing
• balls-and-bins
• fully dynamic
• recourse