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On maximin share allocations in matroids

Gourvès, Laurent; Monnot, Jérôme (2019), On maximin share allocations in matroids, Theoretical Computer Science, 754, p. 50-64. 10.1016/j.tcs.2018.05.018

Type
Article accepté pour publication ou publié
Date
2019
Journal name
Theoretical Computer Science
Volume
754
Publisher
Elsevier
Pages
50-64
Publication identifier
10.1016/j.tcs.2018.05.018
Metadata
Show full item record
Author(s)
Gourvès, Laurent
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Monnot, Jérôme cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
The maximin share guarantee is, in the context of allocating indivisible goods to a set of agents, a recent fairness criterion. A solution achieving a constant approximation of this guarantee always exists and can be computed in polynomial time. We extend the problem to the case where the goods collectively received by the agents satisfy a matroidal constraint. Polynomial approximation algorithms for this generalization are provided: a 1/2-approximation for any number of agents, a (1- ε)-approximation for two agents, and a (8/9 - ε) -approximation for three agents. Apart from the extension to matroids, the (8/9 - ε) -approximation for three agents improves on a (7-8 - ε) -approximation by Amanatidis et al. (ICALP 2015). Some special cases are also presented and some extensions of the model are discussed.
Subjects / Keywords
Approximation algorithms; Fair division; Matroids

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