Abstract
We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents who may have different entitlements. We characterize the existence of a connected strongly-proportional allocation—one in which every agent receives a contiguous piece worth strictly more than their proportional share. The characterization is supplemented with an algorithm that determines its existence using O(n·2n) queries. We devise a simpler characterization for agents with strictly positive valuations and with equal entitlements, and present an algorithm to determine the existence of such an allocation using O(n2) queries. We provide matching lower bounds in the number of queries for both algorithms. When a connected strongly-proportional allocation exists, we show that it can also be computed using a similar number of queries.
| Original language | English |
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| Title of host publication | ECAI 2024 - 27th European Conference on Artificial Intelligence, Including 13th Conference on Prestigious Applications of Intelligent Systems, PAIS 2024, Proceedings |
| Editors | Ulle Endriss, Francisco S. Melo, Kerstin Bach, Alberto Bugarin-Diz, Jose M. Alonso-Moral, Senen Barro, Fredrik Heintz |
| Publisher | IOS Press BV |
| Pages | 3356-3363 |
| Number of pages | 8 |
| ISBN (Electronic) | 9781643685489 |
| DOIs | |
| State | Published - 16 Oct 2024 |
| Externally published | Yes |
| Event | 27th European Conference on Artificial Intelligence, ECAI 2024 - Santiago de Compostela, Spain Duration: 19 Oct 2024 → 24 Oct 2024 |
Publication series
| Name | Frontiers in Artificial Intelligence and Applications |
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| Volume | 392 |
| ISSN (Print) | 0922-6389 |
| ISSN (Electronic) | 1879-8314 |
Conference
| Conference | 27th European Conference on Artificial Intelligence, ECAI 2024 |
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| Country/Territory | Spain |
| City | Santiago de Compostela |
| Period | 19/10/24 → 24/10/24 |
Bibliographical note
Publisher Copyright:© 2024 The Authors.