research-article

Waste Makes Haste: Bounded Time Algorithms for Envy-Free Cake Cutting with Free Disposal

Authors:

Erel Segal-Halevi,

Avinatan Hassidim,

Yonatan AumannAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 13, Issue 1

Article No.: 12, Pages 1 - 32

https://doi.org/10.1145/2988232

Published: 19 November 2016 Publication History

Abstract

We consider the classic problem of envy-free division of a heterogeneous good (“cake”) among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this article, we replace the entire-allocation requirement with a weaker partial-proportionality requirement: the piece given to each agent must be worth for it at least a certain positive fraction of the entire cake value. We prove that this version of the problem is solvable in bounded time even when the pieces must be connected. We present simple, bounded-time envy-free cake-cutting algorithms for (1) giving each of n agents a connected piece with a positive value; (2) giving each of three agents a connected piece worth at least 1/3; (3) giving each of four agents a connected piece worth at least 1/7; (4) giving each of four agents a disconnected piece worth at least 1/4; and (5) giving each of n agents a disconnected piece worth at least (1 − ϵ)/n for any positive ϵ.

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Cited By

Blank MPolyakov M(2024)ELEMENTARNOE REShENIE ZADAChI SPRAVEDLIVOGO DELENIYaProblemy peredači informacii10.31857/S055529232401006660:1(41-59)Online publication date: 15-Dec-2024
https://doi.org/10.31857/S0555292324010066
Blank MPolyakov M(2024)Elementary Solution to the Fair Division ProblemProblems of Information Transmission10.1134/S003294602401006X60:1(53-70)Online publication date: 7-Aug-2024
https://dl.acm.org/doi/10.1134/S003294602401006X
Reitzig RWild S(2024)A simple and fast linear-time algorithm for divisor methods of apportionmentMathematical Programming: Series A and B10.1007/s10107-023-01929-5203:1-2(187-205)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s10107-023-01929-5
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Index Terms

Waste Makes Haste: Bounded Time Algorithms for Envy-Free Cake Cutting with Free Disposal
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 13, Issue 1

January 2017

422 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2997037

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2016 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 November 2016

Accepted: 01 August 2016

Received: 01 December 2015

Published in TALG Volume 13, Issue 1

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Cited By

Blank MPolyakov M(2024)ELEMENTARNOE REShENIE ZADAChI SPRAVEDLIVOGO DELENIYaProblemy peredači informacii10.31857/S055529232401006660:1(41-59)Online publication date: 15-Dec-2024
https://doi.org/10.31857/S0555292324010066
Blank MPolyakov M(2024)Elementary Solution to the Fair Division ProblemProblems of Information Transmission10.1134/S003294602401006X60:1(53-70)Online publication date: 7-Aug-2024
https://dl.acm.org/doi/10.1134/S003294602401006X
Reitzig RWild S(2024)A simple and fast linear-time algorithm for divisor methods of apportionmentMathematical Programming: Series A and B10.1007/s10107-023-01929-5203:1-2(187-205)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s10107-023-01929-5
Bertram NLai THsu J(2024)Verifying Cake-Cutting, FasterComputer Aided Verification10.1007/978-3-031-65630-9_6(109-129)Online publication date: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65630-9_6
Bertram NLevinson AHsu J(2023)Cutting the Cake: A Language for Fair DivisionProceedings of the ACM on Programming Languages10.1145/35912937:PLDI(1779-1800)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591293
Reitzig RWild S(2018)Building Fences Straight and HighAlgorithmica10.1007/s00453-017-0392-380:11(3365-3396)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s00453-017-0392-3
Abebe RKleinberg JParkes DLarson KWinikoff MDas SDurfee E(2017)Fair Division via Social ComparisonProceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems10.5555/3091125.3091171(281-289)Online publication date: 8-May-2017
https://dl.acm.org/doi/10.5555/3091125.3091171
Procaccia AWang JDaskalakis CBabaioff MMoulin H(2017)A Lower Bound for Equitable Cake CuttingProceedings of the 2017 ACM Conference on Economics and Computation10.1145/3033274.3085107(479-495)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.1145/3033274.3085107

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