Algorithmic mechanism design (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
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
Autonomous Agents and Multi-Agent Systems
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The resource allocation problem deals with distributing a number of indivisible, nonshareable resources among a set of agents so as to optimizing social welfare. Assuming all agents to have additive utility functions and focusing on two particular measures of social welfare, envy-ratio and average-Nash product, we investigate the two resulting optimization problems. We give the first hardness of approximation result for a factor better than 3/2 for the problem of minimum envy-ratio, and we design an FPTAS for the case when the number of agents is fixed. For the special case when the number of agents and the number of resources are equal, we show that the problem is even solvable in polynomial time. Next, we propose the first approximation algorithm for maximizing the average-Nash product in the general case, and we prove that this problem admits a PTAS if all agents' utility functions are the same. Finally, we study the problem of how hard it is to design a truthful mechanism for these two optimization problems.