Contiguous Cake Cutting: Hardness Results and Approximation Algorithms - Goldberg, Paul W.; Hollender, Alexandros; Suksompong, Warut (Proceedings of the AAAI Conference on Artificial Intelligence, 2020)
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 strengthening those from prior work.