
Nash Social Welfare for 2value Instances
We study the problem of allocating a set of indivisible goods among agen...
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Approximating Nash Social Welfare under Binary XOS and Binary Subadditive Valuations
We study the problem of allocating indivisible goods among agents in a f...
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Online Nash Social Welfare via Promised Utilities
We consider the problem of allocating a set of divisible goods to N agen...
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Anonymous Hedonic Game for Task Allocation in a LargeScale Multiple Agent System
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Finding Fair and Efficient Allocations When Valuations Don't Add Up
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The HyllandZeckhauser Rule Under BiValued Utilities
The HyllandZeckhauser (HZ) rule is a wellknown rule for probabilistic ...
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Budgetfeasible Maximum Nash Social Welfare Allocation is Almost Envyfree
The Nash social welfare (NSW) is a wellknown social welfare measurement...
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Approximating Nash Social Welfare in 2Valued Instances
We consider the problem of maximizing the Nash social welfare when allocating a set 𝒢 of goods to a set 𝒩 of agents. We study instances, in which all agents have 2valued additive valuations. In such an instance, the value of every agent i ∈𝒩 for every item j ∈𝒢 is v_ij∈{p,q}, for p ≤ q ∈ℕ. We show that an optimal allocation can be computed in polynomial time if p divides q. When p does not divide q, we show an approximation ratio of at most 1.033. It strictly decreases with the denominator of the irreducible fraction that equals p/q. Finally, we prove an APXhardness result for the problem with a lower bound on the ratio of 1.000015.
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