The problem of fair division of indivisible goods is a fundamental problem of social choice. Recently, the problem was extended to the case when goods form a graph and the goal is to allocate goods to agents so that each agent's bundle forms a connected subgraph. For the maximin share fairness criterion researchers proved that if goods form a tree, allocations offering each agent a bundle of at least her maximin share value always exist. Moreover, they can be found in polynomial time. We consider here the problem of maximin share allocations of goods on a cycle. Despite the simplicity of the graph, the problem turns out to be significantly harder than its tree version. We present cases when maximin share allocations of goods on cycles exist and provide results on allocations guaranteeing each agent a certain portion of her maximin share. We also study algorithms for computing maximin share allocations of goods on cycles.
|Title of host publication||Proceedings of the 27th International Joint Conference on Artificial Intelligence, IJCAI 2018|
|Number of pages||7|
|State||Published - 2018|
|Event||27th International Joint Conference on Artificial Intelligence, IJCAI 2018 - Stockholm, Sweden|
Duration: Jul 13 2018 → Jul 19 2018
|Name||IJCAI International Joint Conference on Artificial Intelligence|
|Conference||27th International Joint Conference on Artificial Intelligence, IJCAI 2018|
|Period||7/13/18 → 7/19/18|
Bibliographical noteFunding Information:
The work of the second author was partially supported by the NSF grant IIS-1618783.
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ASJC Scopus subject areas
- Artificial Intelligence