Dynamic Necklace Splitting
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913160769830912 |
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| author | Advani, Rishi Asudeh, Abolfazl Dehghankar, Mohsen Sintos, Stavros |
| author_facet | Advani, Rishi Asudeh, Abolfazl Dehghankar, Mohsen Sintos, Stavros |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamic Necklace Splitting Advani, Rishi Asudeh, Abolfazl Dehghankar, Mohsen Sintos, Stavros Computer Science and Game Theory Discrete Mathematics Data Structures and Algorithms F.2.2; G.2.m 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. |
| title | Dynamic Necklace Splitting |
| topic | Computer Science and Game Theory Discrete Mathematics Data Structures and Algorithms F.2.2; G.2.m |
| url | https://arxiv.org/abs/2510.00162 |