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arXiv · 2510.00162

Dynamic Necklace Splitting

Rishi Advani·Abolfazl Asudeh·Mohsen Dehghankar·Stavros Sintos
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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.

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Rishi Advani, Abolfazl Asudeh, Mohsen Dehghankar, Stavros Sintos. 2025-09-30. Dynamic Necklace Splitting. https://doi.org/10.4230/lipics.icdt.2026.19

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