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DOI: 10.4230/OASIcs.SOSA.2019.20
URN: urn:nbn:de:0030-drops-100465
URL: http://drops.dagstuhl.de/opus/volltexte/2018/10046/
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Garg, Jugal ; McGlaughlin, Peter ; Taki, Setareh

Approximating Maximin Share Allocations

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OASIcs-SOSA-2019-20.pdf (0.4 MB)


Abstract

We study the problem of fair allocation of M indivisible items among N agents using the popular notion of maximin share as our measure of fairness. The maximin share of an agent is the largest value she can guarantee herself if she is allowed to choose a partition of the items into N bundles (one for each agent), on the condition that she receives her least preferred bundle. A maximin share allocation provides each agent a bundle worth at least their maximin share. While it is known that such an allocation need not exist [Procaccia and Wang, 2014; Kurokawa et al., 2016], a series of work [Procaccia and Wang, 2014; David Kurokawa et al., 2018; Amanatidis et al., 2017; Barman and Krishna Murthy, 2017] provided 2/3 approximation algorithms in which each agent receives a bundle worth at least 2/3 times their maximin share. Recently, [Ghodsi et al., 2018] improved the approximation guarantee to 3/4. Prior works utilize intricate algorithms, with an exception of [Barman and Krishna Murthy, 2017] which is a simple greedy solution but relies on sophisticated analysis techniques. In this paper, we propose an alternative 2/3 maximin share approximation which offers both a simple algorithm and straightforward analysis. In contrast to other algorithms, our approach allows for a simple and intuitive understanding of why it works.

BibTeX - Entry

@InProceedings{garg_et_al:OASIcs:2018:10046,
  author =	{Jugal Garg and Peter McGlaughlin and Setareh Taki},
  title =	{{Approximating Maximin Share Allocations}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{20:1--20:11},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{69},
  editor =	{Jeremy T. Fineman and Michael Mitzenmacher},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10046},
  URN =		{urn:nbn:de:0030-drops-100465},
  doi =		{10.4230/OASIcs.SOSA.2019.20},
  annote =	{Keywords: Fair division, Maximin share, Approximation algorithm}
}

Keywords: Fair division, Maximin share, Approximation algorithm
Seminar: 2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Issue Date: 2018
Date of publication: 18.12.2018


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