Contiguous Cake Cutting: Hardness Results and Approximation Algorithms
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.
Cite
@article{arxiv.1911.05416,
title = {Contiguous Cake Cutting: Hardness Results and Approximation Algorithms},
author = {Paul W. Goldberg and Alexandros Hollender and Warut Suksompong},
journal= {arXiv preprint arXiv:1911.05416},
year = {2020}
}
Comments
Appears in the 34th AAAI Conference on Artificial Intelligence (AAAI), 2020