The Query Complexity of Cake Cutting

Simina Brânzei, Noam Nisan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

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 languageAmerican English
Title of host publicationAdvances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
EditorsS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
PublisherNeural information processing systems foundation
ISBN (Electronic)9781713871088
StatePublished - 2022
Event36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States
Duration: 28 Nov 20229 Dec 2022

Publication series

NameAdvances in Neural Information Processing Systems
Volume35
ISSN (Print)1049-5258

Conference

Conference36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/TerritoryUnited States
CityNew Orleans
Period28/11/229/12/22

Bibliographical note

Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.

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