Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Thou shalt covet thy neighbor's cake
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
The Efficiency of Fair Division
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On Allocating Goods to Maximize Fairness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Strategy-proof allocation of multiple items between two agents without payments or priors
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
The efficiency of fair division with connected pieces
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Can trust increase the efficiency of cake cutting algorithms?
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 3
On strategy-proof allocation without payments or priors
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Incentive compatible two player cake cutting
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Parameterized Complexity
Cake cutting: not just child's play
Communications of the ACM
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A frequent task facing a MAS designer is to efficiently divide resources amongst multiple agents. We consider a setting in which a single divisible resource, a.k.a. "cake", needs to be divided amongst n agents, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the social welfare, focusing on divisions where each agent gets a single contiguous piece of the cake. We provide a constant factor approximation algorithm for the problem, and prove that it is NP-hard to find the optimal division, and that the problem admits no FPTAS unless P=NP. These results hold both when the full valuations of all agents are given to the algorithm, and when the algorithm has only oracle access to the valuation functions. In contrast, if agents can get multiple, non-contiguous pieces of the cake, the results vary greatly depending on the input model. If the algorithm is provided with the full valuation functions of all agents, then the problem is easy. However, if the algorithm needs to query the agents for information on their valuations, then no non-trivial approximation (i.e.