We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed; however, in the latter case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.
|Title of host publication
|Proceedings of the 30th International Joint Conference on Artificial Intelligence, IJCAI 2021
|International Joint Conferences on Artificial Intelligence
|Number of pages
|Published - 2021
|30th International Joint Conference on Artificial Intelligence, IJCAI 2021 - Virtual, Online, Canada
Duration: 19 Aug 2021 → 27 Aug 2021
|IJCAI International Joint Conference on Artificial Intelligence
|30th International Joint Conference on Artificial Intelligence, IJCAI 2021
|19/08/21 → 27/08/21
Bibliographical notePublisher Copyright:
© 2021 International Joint Conferences on Artificial Intelligence. All rights reserved.