Abstract
We consider the query complexity of cake cutting in the standard query model and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing contiguous envy-free allocations among n = 3 players and for computing perfect and equitable allocations with minimum number of cuts between n = 2 players. For ϵ-envy-free allocations with contiguous pieces, we also give an upper bound of O(n/ϵ) and lower bound of Ω(log(1/ϵ)) queries for any number n ≥ 3 of players. We also formalize moving knife procedures and show that a large subclass of this family, which captures all the known moving knife procedures, can be simulated efficiently with arbitrarily small error in the Robertson-Webb query model.
| Original language | English |
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| Title of host publication | Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022 |
| Editors | S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh |
| Publisher | Neural information processing systems foundation |
| ISBN (Electronic) | 9781713871088 |
| State | Published - 2022 |
| Event | 36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States Duration: 28 Nov 2022 → 9 Dec 2022 |
Publication series
| Name | Advances in Neural Information Processing Systems |
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| Volume | 35 |
| ISSN (Print) | 1049-5258 |
Conference
| Conference | 36th Conference on Neural Information Processing Systems, NeurIPS 2022 |
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| Country/Territory | United States |
| City | New Orleans |
| Period | 28/11/22 → 9/12/22 |
Bibliographical note
Publisher Copyright:© 2022 Neural information processing systems foundation. All rights reserved.