TY - JOUR
T1 - Computing welfare-Maximizing fair allocations of indivisible goods
AU - Aziz, Haris
AU - Huang, Xin
AU - Mattei, Nicholas
AU - Segal-Halevi, Erel
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents’ utilities. We focus on two tractable fairness concepts: envy-freeness up to one item (EF1) and proportionality up to one item (PROP1). We consider two computational problems: (1) Among the utilitarian-maximal allocations, decide whether there exists one that is also fair; (2) among the fair allocations, compute one that maximizes the utilitarian welfare. We show that both problems are strongly NP-hard when the number of agents is variable, and remain NP-hard for a fixed number of agents greater than two. For the special case of two agents, we find that problem (1) is polynomial-time solvable, while problem (2) remains NP-hard. Finally, with a fixed number of agents, we design pseudopolynomial-time algorithms for both problems. We extend our results to the stronger fairness notions envy-freeness up to any item (EFx) and proportionality up to any item (PROPx).
AB - We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents’ utilities. We focus on two tractable fairness concepts: envy-freeness up to one item (EF1) and proportionality up to one item (PROP1). We consider two computational problems: (1) Among the utilitarian-maximal allocations, decide whether there exists one that is also fair; (2) among the fair allocations, compute one that maximizes the utilitarian welfare. We show that both problems are strongly NP-hard when the number of agents is variable, and remain NP-hard for a fixed number of agents greater than two. For the special case of two agents, we find that problem (1) is polynomial-time solvable, while problem (2) remains NP-hard. Finally, with a fixed number of agents, we design pseudopolynomial-time algorithms for both problems. We extend our results to the stronger fairness notions envy-freeness up to any item (EFx) and proportionality up to any item (PROPx).
KW - Assignment
KW - Fair division
KW - Group decisions and negotiations
KW - Indivisible items
KW - Utilitarian welfare
UR - http://www.scopus.com/inward/record.url?scp=85140782651&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2022.10.013
DO - 10.1016/j.ejor.2022.10.013
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AN - SCOPUS:85140782651
SN - 0377-2217
VL - 307
SP - 773
EP - 784
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -