History-Independent Load Balancing

TL;DR

This work resolves a central question in dynamic load balancing by producing a strongly history-independent two-choice allocator that handles insertions and deletions for up to $m$ balls on $n$ bins while guaranteeing an overload of $m/n + O(1)$ with high probability and an expected recourse of $O(\log\log (m/n))$. The construction combines a history-independent greedy baseline with a novel slice-and-spread gadget to reduce overload, followed by a postprocessing ECO-based step that enforces a constant overload without sacrificing recourse. The resulting algorithm improves on history-dependent bounds and presents a principled approach that leverages the history-independence paradigm to achieve strong guarantees in fully dynamic settings. This advances both theoretical understanding and potential practical deployment of privacy-aware dynamic load balancing, and connects history independence with powerful algorithmic techniques such as cuckoo-hashing-inspired graph orientation and ECO postprocessing.

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 $m/n \ge ω(1)$ and is the first fully dynamic solution (history independent or not) to achieve $O(1)$ overload with $o(m/n)$ expected recourse.

Theorems & Definitions (95)

• Theorem 1.1
• Proposition 3.1
• proof
• proof
• Proposition 3.2
• Theorem 4.1
• Proposition 4.1
• Lemma 4.2
• proof
• Lemma 4.3