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Dynamic Necklace Splitting

Authors Rishi Advani , Abolfazl Asudeh , Mohsen Dehghankar , Stavros Sintos

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LIPIcs.ICDT.2026.19.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → Algorithmic game theory
Keywords
  • Necklace splitting
  • dynamic algorithms
  • fair division

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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.

Cite As Get BibTex

Rishi Advani, Abolfazl Asudeh, Mohsen Dehghankar, and Stavros Sintos. Dynamic Necklace Splitting. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICDT.2026.19

Author Details

Rishi Advani
  • University of Illinois Chicago, IL, USA
Abolfazl Asudeh
  • University of Illinois Chicago, IL, USA
Mohsen Dehghankar
  • University of Illinois Chicago, IL, USA
Stavros Sintos
  • University of Illinois Chicago, IL, USA

Funding

This material is based upon work supported by the U.S. National Science Foundation under award No. 2348919.
  • Advani, Rishi: This author was supported by the UIC University Fellowship.

Acknowledgements

We would like to thank the reviewers for their constructive feedback.

References

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