Graph minimal uncolorability is DP-complete
SIAM Journal on Computing
More complicated questions about maxima and minima, and some closures of NP
Theoretical Computer Science
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
The Boolean hierarchy I: structural properties
SIAM Journal on Computing
The Boolean hierarchy II: applications
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
k-order additive discrete fuzzy measures and their representation
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Relations Among Complexity Measures
Journal of the ACM (JACM)
Truth revelation in approximately efficient combinatorial auctions
Proceedings of the 1st ACM conference on Electronic commerce
Some optimal inapproximability results
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exact complexity of exact-four-colorability
Information Processing Letters
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Allocation of indivisible goods: a general model and some complexity results
Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
Complexity Theory and Cryptology
Complexity Theory and Cryptology
ACM SIGecom Exchanges
Combinatorial auctions with k-wise dependent valuations
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
The complexity of contract negotiation
Artificial Intelligence
Complexity of social welfare optimization in multiagent resource allocation
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
Complexity and approximability of social welfare optimization in multiagent resource allocation
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
Envy-ratio and average-nash social welfare optimization in multiagent resource allocation
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle form, the $$k$$ k -additive form, and as straight-line programs. We study the computational complexity of social welfare optimization in multiagent resource allocation, where we consider utilitarian and egalitarian social welfare and social welfare by the Nash product. Solving some of the open problems raised by Chevaleyre et al. (2006) and confirming their conjectures, we prove that egalitarian social welfare optimization is $$\mathrm{NP}$$ NP -complete for the bundle form, and both exact utilitarian and exact egalitarian social welfare optimization are $$\mathrm{DP}$$ DP -complete, each for both the bundle and the $$2$$ 2 -additive form, where $$\mathrm{DP}$$ DP is the second level of the boolean hierarchy over $$\mathrm{NP}$$ NP . In addition, we prove that social welfare optimization by the Nash product is $$\mathrm{NP}$$ NP -complete for both the bundle and the $$1$$ 1 -additive form, and that the exact variants are $$\mathrm{DP}$$ DP -complete for the bundle and the $$3$$ 3 -additive form. For utility functions represented as straight-line programs, we show $$\mathrm{NP}$$ NP -completeness for egalitarian social welfare optimization and social welfare optimization by the Nash product. Finally, we show that social welfare optimization by the Nash product in the $$1$$ 1 -additive form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the $$1$$ 1 -additive form with a fixed number of agents.