Article

Algorithms for max-min share fair allocation of indivisible chores

Authors:

Gerhard Rauchecker,

Toby WalshAuthors Info & Claims

AAAI'17: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence

Pages 335 - 341

Published: 04 February 2017 Publication History

Abstract

We consider Max-min Share (MmS) fair allocations of indivisible chores (items with negative utilities). We show that allocation of chores and classical allocation of goods (items with positive utilities) have some fundamental connections but also differences which prevent a straightforward application of algorithms for goods in the chores setting and vice-versa. We prove that an MmS allocation does not need to exist for chores and computing an MmS allocation - if it exists - is strongly NP-hard. In view of these non-existence and complexity results, we present a polynomial-time 2-approximation algorithm for MmS fairness for chores. We then introduce a new fairness concept called optimal MmS that represents the best possible allocation in terms of MmS that is guaranteed to exist. We use connections to parallel machine scheduling to give (1) a polynomial-time approximation scheme for computing an optimal MmS allocation when the number of agents is fixed and (2) an effective and efficient heuristic with an ex-post worst-case analysis.

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Cited By

Hosseini HSikdar SVaish RXia LAgmon NAn BRicci AYeoh W(2023)Fairly Dividing Mixtures of Goods and Chores under Lexicographic PreferencesProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598632(152-160)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598632
Hosseini HMammadov AWąs TElkind E(2023)Fairly allocating goods and (terrible) choresProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/305(2738-2746)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/305
Feige UHuang XLeyton-Brown KSamuelson LHartline J(2023)On picking sequences for choresProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597783(626-655)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597783
Show More Cited By

Algorithms for max-min share fair allocation of indivisible chores
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
    2. Online algorithms
      1. Online learning algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning

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cover image Guide Proceedings

AAAI'17: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence

February 2017

5106 pages

Program Chairs:
Satinder Singh
University of Michigan
,
Shaul Markovitch
Technion-Israel Institute of Technology

Sponsors

Association for the Advancement of Artificial Intelligence
amazon: amazon
Infosys
Facebook: Facebook
IBM: IBM

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AAAI Press

Publication History

Published: 04 February 2017

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Cited By

Hosseini HSikdar SVaish RXia LAgmon NAn BRicci AYeoh W(2023)Fairly Dividing Mixtures of Goods and Chores under Lexicographic PreferencesProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems10.5555/3545946.3598632(152-160)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.5555/3545946.3598632
Hosseini HMammadov AWąs TElkind E(2023)Fairly allocating goods and (terrible) choresProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/305(2738-2746)Online publication date: 19-Aug-2023
https://dl.acm.org/doi/10.24963/ijcai.2023/305
Feige UHuang XLeyton-Brown KSamuelson LHartline J(2023)On picking sequences for choresProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597783(626-655)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597783
Chaudhury BGarg JMcGlaughlin PMehta RMarx D(2021)Competitive allocation of a mixed mannaProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458149(1405-1424)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458149
Huang XLu PBiró PChawla SEchenique F(2021)An Algorithmic Framework for Approximating Maximin Share Allocation of ChoresProceedings of the 22nd ACM Conference on Economics and Computation10.1145/3465456.3467555(630-631)Online publication date: 18-Jul-2021
https://dl.acm.org/doi/10.1145/3465456.3467555
Li BLi YEl Fallah Seghrouchni ASukthankar GAn BYorke-Smith N(2020)Fair Resource Sharing and Dorm AssignmentProceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems10.5555/3398761.3398846(708-716)Online publication date: 5-May-2020
https://dl.acm.org/doi/10.5555/3398761.3398846
Aziz HLi BWu X(2019)Strategyproof and approximately maxmin fair share allocation of choresProceedings of the 28th International Joint Conference on Artificial Intelligence10.5555/3367032.3367042(60-66)Online publication date: 10-Aug-2019
https://dl.acm.org/doi/10.5555/3367032.3367042
Aziz HChan HLi B(2019)Weighted maxmin fair share allocation of indivisible choresProceedings of the 28th International Joint Conference on Artificial Intelligence10.5555/3367032.3367040(46-52)Online publication date: 10-Aug-2019
https://dl.acm.org/doi/10.5555/3367032.3367040
Aziz HChan HLi BElkind EVeloso MAgmon NTaylor M(2019)Maxmin Share Fair Allocation of Indivisible Chores to Asymmetric AgentsProceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems10.5555/3306127.3331919(1787-1789)Online publication date: 8-May-2019
https://dl.acm.org/doi/10.5555/3306127.3331919
Seddighin MSaleh HGhodsi M(2019)Externalities and FairnessThe World Wide Web Conference10.1145/3308558.3313670(538-548)Online publication date: 13-May-2019
https://dl.acm.org/doi/10.1145/3308558.3313670

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