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arXiv · 1911.05416

Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

Paul W. Goldberg·Alexandros Hollender·Warut Suksompong
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Abstract

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results extending and strengthening those from prior work. Finally, we investigate connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting.

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Paul W. Goldberg, Alexandros Hollender, Warut Suksompong. 2019-11-13. Contiguous Cake Cutting: Hardness Results and Approximation Algorithms. https://doi.org/10.1613/jair.1.12222

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