TY - JOUR
T1 - Multivariate algorithmics for eliminating envy by donating goods
AU - Boehmer, Niclas
AU - Bredereck, Robert
AU - Heeger, Klaus
AU - Knop, Dušan
AU - Luo, Junjie
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/12/1
Y1 - 2024/12/1
N2 - Fairly dividing a set of indivisible resources to a set of agents is of utmost importance in some applications. However, after an allocation has been implemented the preferences of agents might change and envy might arise. We study the following problem to cope with such situations: given an allocation of indivisible resources to agents with additive utility-based preferences, is it possible to socially donate some of the resources (which means removing these resources from the allocation instance) such that the resulting modified allocation is envy-free (up to one good). We require that the number of deleted resources and/or the caused utilitarian welfare loss of the allocation are bounded. We conduct a thorough study of the (parameterized) computational complexity of this problem considering various natural and problem-specific parameters (e.g., the number of agents, the number of deleted resources, or the maximum number of resources assigned to an agent in the initial allocation) and different preference models, including unary-encoded and 0/1-valuations. In our studies, we obtain a rich set of (parameterized) tractability and intractability results and discover several surprising contrasts, for instance, between the two closely related fairness concepts envy-freeness and envy-freeness up to one good and between the influence of the parameters maximum number and welfare of the deleted resources.
AB - Fairly dividing a set of indivisible resources to a set of agents is of utmost importance in some applications. However, after an allocation has been implemented the preferences of agents might change and envy might arise. We study the following problem to cope with such situations: given an allocation of indivisible resources to agents with additive utility-based preferences, is it possible to socially donate some of the resources (which means removing these resources from the allocation instance) such that the resulting modified allocation is envy-free (up to one good). We require that the number of deleted resources and/or the caused utilitarian welfare loss of the allocation are bounded. We conduct a thorough study of the (parameterized) computational complexity of this problem considering various natural and problem-specific parameters (e.g., the number of agents, the number of deleted resources, or the maximum number of resources assigned to an agent in the initial allocation) and different preference models, including unary-encoded and 0/1-valuations. In our studies, we obtain a rich set of (parameterized) tractability and intractability results and discover several surprising contrasts, for instance, between the two closely related fairness concepts envy-freeness and envy-freeness up to one good and between the influence of the parameters maximum number and welfare of the deleted resources.
KW - Donating goods
KW - Envy-freeness
KW - Fair allocation
KW - Indivisible resources
KW - Parameterized algorithmics
UR - http://www.scopus.com/inward/record.url?scp=85203354469&partnerID=8YFLogxK
U2 - 10.1007/s10458-024-09674-5
DO - 10.1007/s10458-024-09674-5
M3 - Article
AN - SCOPUS:85203354469
SN - 1387-2532
VL - 38
JO - Autonomous Agents and Multi-Agent Systems
JF - Autonomous Agents and Multi-Agent Systems
IS - 2
M1 - 43
ER -