Agreeable sets with matroidal constraints
Gourvès, Laurent (2019), Agreeable sets with matroidal constraints, Journal of Combinatorial Optimization, 37, 3, p. 866-888. 10.1007/s10878-018-0327-1
TypeArticle accepté pour publication ou publié
Journal nameJournal of Combinatorial Optimization
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)This article deals with the challenge of reaching an agreement for a group of agents who have heterogeneous preferences over a set of goods. In a recent work, Suksompong (in: Subbarao (ed) Proceedings of the twenty-fifth international joint conference on artificial intelligence, IJCAI 2016, New York, pp 489–495, 2016) models a problem of this kind as the search of an agreeable subset of a given ground set of goods. A subset is agreeable if it is weakly preferred to its complement by every agent of the group. Under natural assumptions on the agents’ preferences such as monotonicity or responsiveness, an agreeable set of small cardinality is guaranteed to exist, and it can be efficiently computed. This article deals with an extension to subsets which must satisfy extra matroidal constraints. Worst case upper bounds on the size of an agreeable set are shown, and algorithms for computing them are given. For the case of two agents having additive preferences, we show that an agreeable solution can also be approximately optimal (up to a multiplicative constant factor) for both agents.
Subjects / KeywordsAllocation of indivisible goods; Matroids; Approximation
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