The maximin share guarantee is, in the context of allocating indivisible goods to a set of agents, a recent fairness criterion. A solu-tion 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 gen-eralization 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).
CITATION STYLE
Gourvès, L., & Monnot, J. (2017). Approximate maximin share allocations in matroids. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10236 LNCS, pp. 310–321). Springer Verlag. https://doi.org/10.1007/978-3-319-57586-5_26
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