Allocating Indivisible Items with Minimum Dissatisfaction on Preference Graphs

Chiarelli, Nina; Dallard, Clément; Darmann, Andreas; Lendl, Stefan; Milanič, Martin; Mursic, Peter; Pivač, Nevena; Pferschy, Ulrich

doi:10.1007/978-3-030-87756-9_16

Cited by 2 publications

(1 citation statement)

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“…Furthermore, a fixed-parameter tractability result can be shown with respect to the treewidth of the union of preference graphs and the number of agents. A preliminary version of this work containing some of the results and omitting most of the proofs appeared as [12].…”

Section: Introductionmentioning

confidence: 99%

Allocation of Indivisible Items with Individual Preference Graphs

Chiarelli¹,

Dallard²,

Darmann³

et al. 2022

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This paper studies the allocation of indivisible items to agents, when each agent's preferences are expressed by means of a directed acyclic graph. The vertices of each preference graph represent the subset of items approved of by the respective agent. An arc (a, b) in such a graph means that the respective agent prefers item a over item b. We introduce a new measure of dissatisfaction of an agent by counting the number of non-assigned items which are approved of by the agent and for which no more preferred item is allocated to the agent. Considering two problem variants, we seek an allocation of the items to the agents in a way that minimizes (i) the total dissatisfaction over all agents or (ii) the maximum dissatisfaction among the agents. For both optimization problems we study the status of computational complexity and obtain NP-hardness results as well as polynomial algorithms with respect to natural underlying graph structures, such as stars, trees, paths, and matchings. We also analyze the parameterized complexity of the two problems with respect to various parameters related to the number of agents, the dissatisfaction threshold, the vertex degrees of the preference graphs, and the treewidth.

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Section: Introductionmentioning

confidence: 99%