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A Lower Bound for Equitable Cake Cutting

Published: 20 June 2017 Publication History

Abstract

We are interested in the problem of dividing a cake -- a heterogeneous divisible good -- among n players, in a way that is ε-equitable: every pair of players must have the same value for their own allocated pieces, up to a difference of at most ε. It is known that such allocations can be computed using O(n ln(1/ε)) operations in the standard Robertson-Webb Model. We establish a lower bound of Ω(ln(1/ε)/lnln(1/ε)) on the complexity of this problem, which is almost tight for a constant number of players. Importantly, our result implies that allocations that are exactly equitable cannot be computed.

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  • (2024)Connected Equitable Cake Division via Sperner's LemmaInformation Processing Letters10.1016/j.ipl.2024.106554(106554)Online publication date: Dec-2024
  • (2023)Envy-Free Cake-Cutting for Four Agents2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00015(113-122)Online publication date: 6-Nov-2023
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cover image ACM Conferences
EC '17: Proceedings of the 2017 ACM Conference on Economics and Computation
June 2017
740 pages
ISBN:9781450345279
DOI:10.1145/3033274
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 20 June 2017

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Author Tags

  1. cake cutting
  2. computational fair division

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EC '17
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EC '17: ACM Conference on Economics and Computation
June 26 - 30, 2017
Massachusetts, Cambridge, USA

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EC '17 Paper Acceptance Rate 75 of 257 submissions, 29%;
Overall Acceptance Rate 664 of 2,389 submissions, 28%

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The 25th ACM Conference on Economics and Computation
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Cited By

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  • (2024)Participatory Objective Design via Preference ElicitationProceedings of the 2024 ACM Conference on Fairness, Accountability, and Transparency10.1145/3630106.3658994(1637-1662)Online publication date: 3-Jun-2024
  • (2024)Connected Equitable Cake Division via Sperner's LemmaInformation Processing Letters10.1016/j.ipl.2024.106554(106554)Online publication date: Dec-2024
  • (2023)Envy-Free Cake-Cutting for Four Agents2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00015(113-122)Online publication date: 6-Nov-2023
  • (2022)Mind the gap: Cake cutting with separationArtificial Intelligence10.1016/j.artint.2022.103783(103783)Online publication date: Sep-2022
  • (2020)Learning the valuations of a k-demand agentProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525964(11066-11075)Online publication date: 13-Jul-2020
  • (2020)Equitable Allocations of Indivisible ChoresProceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems10.5555/3398761.3398810(384-392)Online publication date: 5-May-2020
  • (2019)Equitable allocations of indivisible goodsProceedings of the 28th International Joint Conference on Artificial Intelligence10.5555/3367032.3367073(280-286)Online publication date: 10-Aug-2019
  • (2019)Fair cake-cutting among familiesSocial Choice and Welfare10.1007/s00355-019-01210-9Online publication date: 12-Aug-2019
  • (2018)Resource-monotonicity and population-monotonicity in connected cake-cuttingMathematical Social Sciences10.1016/j.mathsocsci.2018.07.00195(19-30)Online publication date: Sep-2018

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