Fair division of a graph
We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where t...
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| Format: | Conference item |
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AAAI Press / International Joint Conferences on Artificial Intelligence
2017
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| _version_ | 1826298307143532544 |
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| author | Bouveret, S Cechlárová, K Elkind, E Igarashi, A Peters, D |
| author_facet | Bouveret, S Cechlárová, K Elkind, E Igarashi, A Peters, D |
| author_sort | Bouveret, S |
| collection | OXFORD |
| description | We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents-or, less restrictively, the number of agent types-is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently. |
| first_indexed | 2024-03-07T04:44:50Z |
| format | Conference item |
| id | oxford-uuid:d2e20786-3f41-4e4c-b420-cfcf24cc41d5 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:44:50Z |
| publishDate | 2017 |
| publisher | AAAI Press / International Joint Conferences on Artificial Intelligence |
| record_format | dspace |
| spelling | oxford-uuid:d2e20786-3f41-4e4c-b420-cfcf24cc41d52022-03-27T08:07:20ZFair division of a graphConference itemhttp://purl.org/coar/resource_type/c_5794uuid:d2e20786-3f41-4e4c-b420-cfcf24cc41d5Symplectic Elements at OxfordAAAI Press / International Joint Conferences on Artificial Intelligence2017Bouveret, SCechlárová, KElkind, EIgarashi, APeters, DWe consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents-or, less restrictively, the number of agent types-is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently. |
| spellingShingle | Bouveret, S Cechlárová, K Elkind, E Igarashi, A Peters, D Fair division of a graph |
| title | Fair division of a graph |
| title_full | Fair division of a graph |
| title_fullStr | Fair division of a graph |
| title_full_unstemmed | Fair division of a graph |
| title_short | Fair division of a graph |
| title_sort | fair division of a graph |
| work_keys_str_mv | AT bouverets fairdivisionofagraph AT cechlarovak fairdivisionofagraph AT elkinde fairdivisionofagraph AT igarashia fairdivisionofagraph AT petersd fairdivisionofagraph |