Dynamic Necklace Splitting
Computer Science and Game Theory
2026-05-26 v2 Discrete Mathematics
Data Structures and Algorithms
Abstract
The necklace splitting problem is a classic problem in fair division with many applications, including data-informed fair hash maps. We extend necklace splitting to a dynamic setting, allowing for relocation, insertion, and deletion of beads. We present linear-time, optimal algorithms for the two-color case that support all dynamic updates. For more than two colors, we give linear-time, optimal algorithms for relocation subject to a restriction on the number of agents. Finally, we propose a randomized algorithm for the two-color case that handles all dynamic updates, guarantees approximate fairness with high probability, and runs in polylogarithmic time when the number of agents is small.
Keywords
Cite
@article{arxiv.2510.00162,
title = {Dynamic Necklace Splitting},
author = {Rishi Advani and Abolfazl Asudeh and Mohsen Dehghankar and Stavros Sintos},
journal= {arXiv preprint arXiv:2510.00162},
year = {2026}
}
Comments
20 pages, 5 figures