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 | American 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
Funding Information:We thank the reviewers for helpful feedback. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement no. 740282). A part of this work was done while Simina Brânzei was visiting the Simons Institute for the Theory of Computing.
Funding Information:
Acknowledgements We thank the reviewers for helpful feedback. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 740282). A part of this work was done while Simina Brânzei was visiting the Simons Institute for the Theory of Computing.
Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.