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Article

An approximation algorithm for max-min fair allocation of indivisible goods

Authors:

Arash Asadpour,

Amin SaberiAuthors Info & Claims

STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing

Pages 114 - 121

https://doi.org/10.1145/1250790.1250808

Published: 11 June 2007 Publication History

Abstract

In this paper we give the first approximation algorithm for the problem of max-min fair allocation of indivisible goods. The approximation ratio of our algorithm is Ω1√k log³ k. As a part of our algorithm, we design an iterative method for rounding a fractional matching on a tree which might be of independent interest.

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Cited By

Verma SZhao YShah SBoehmer NTaneja ATambe MKiyavash NMooij J(2024)Group fairness in predict-then-optimize settings for restless banditsProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702839(3448-3469)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.5555/3702676.3702839
Brown ALaddha ASingh M(2024)Fast Algorithms for Maximizing the Minimum Eigenvalue in Fixed DimensionOperations Research Letters10.1016/j.orl.2024.107186(107186)Online publication date: Sep-2024
https://doi.org/10.1016/j.orl.2024.107186
Ding GBalakrishnan H(2023)Lexicographic Min-Max Fairness in Task Assignments2023 62nd IEEE Conference on Decision and Control (CDC)10.1109/CDC49753.2023.10384128(3408-3414)Online publication date: 13-Dec-2023
https://doi.org/10.1109/CDC49753.2023.10384128
Show More Cited By

Index Terms

An approximation algorithm for max-min fair allocation of indivisible goods
1. Theory of computation
  1. Randomness, geometry and discrete structures

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The problem of allocating divisible goods has enjoyed a lot of attention in both mathematics (e.g. the cake-cutting problem) and economics (e.g. market equilibria). On the other hand, the natural requirement of indivisible goods has been somewhat ...
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods

In this paper, we give the first approximation algorithm for the problem of max-min fair allocation of indivisible goods. An instance of this problem consists of a set of $k$ people and $m$ indivisible goods. Each person has a known linear utility ...

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Published In

cover image ACM Conferences

STOC '07: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing

June 2007

734 pages

ISBN:9781595936318

DOI:10.1145/1250790

General Chair:
David Johnson
AT&T Labs - Research
,
Program Chair:
Uriel Feige
Microsoft Research and Weizmann Institute

Copyright © 2007 ACM.

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 ACM 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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Published: 11 June 2007

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STOC07: Symposium on Theory of Computing

June 11 - 13, 2007

California, San Diego, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Verma SZhao YShah SBoehmer NTaneja ATambe MKiyavash NMooij J(2024)Group fairness in predict-then-optimize settings for restless banditsProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702839(3448-3469)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.5555/3702676.3702839
Brown ALaddha ASingh M(2024)Fast Algorithms for Maximizing the Minimum Eigenvalue in Fixed DimensionOperations Research Letters10.1016/j.orl.2024.107186(107186)Online publication date: Sep-2024
https://doi.org/10.1016/j.orl.2024.107186
Ding GBalakrishnan H(2023)Lexicographic Min-Max Fairness in Task Assignments2023 62nd IEEE Conference on Decision and Control (CDC)10.1109/CDC49753.2023.10384128(3408-3414)Online publication date: 13-Dec-2023
https://doi.org/10.1109/CDC49753.2023.10384128
Ko SChen HCheng SHon WLiao C(2023)Polynomial-time Combinatorial Algorithm for General Max–Min Fair AllocationAlgorithmica10.1007/s00453-023-01105-386:2(485-504)Online publication date: 27-Feb-2023
https://doi.org/10.1007/s00453-023-01105-3
Cheng SMao Y(2022)Restricted Max-Min Allocation: Integrality Gap and Approximation AlgorithmAlgorithmica10.1007/s00453-022-00942-y84:7(1835-1874)Online publication date: 23-Feb-2022
https://doi.org/10.1007/s00453-022-00942-y
Ghodsi MHajiaghayi MSeddighin MSeddighin SYami H(2021)Fair Allocation of Indivisible GoodsMathematics of Operations Research10.1287/moor.2020.109646:3(1038-1053)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1287/moor.2020.1096
Ko SChen HCheng SHon WLiao C(2021)General Max-Min Fair AllocationComputing and Combinatorics10.1007/978-3-030-89543-3_6(63-75)Online publication date: 20-Oct-2021
https://doi.org/10.1007/978-3-030-89543-3_6
Bouveret SLang JLemaître M(2020)Collective Decision MakingA Guided Tour of Artificial Intelligence Research10.1007/978-3-030-06164-7_18(587-627)Online publication date: 8-May-2020
https://doi.org/10.1007/978-3-030-06164-7_18
Heinen TNguyen NNguyen TRothe J(2018)Approximation and complexity of the optimization and existence problems for maximin share, proportional share, and minimax share allocation of indivisible goodsAutonomous Agents and Multi-Agent Systems10.5555/3288249.328826032:6(741-778)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288249.3288260
Ghodsi MHajiaghayi MSeddighin MSeddighin SYami HTardos EElkind EVohra R(2018)Fair Allocation of Indivisible GoodsProceedings of the 2018 ACM Conference on Economics and Computation10.1145/3219166.3219238(539-556)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3219166.3219238
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