Welfare Loss in Connected Resource Allocation
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908773586567168 |
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| author | Bei, Xiaohui Lam, Alexander Lu, Xinhang Suksompong, Warut |
| author_facet | Bei, Xiaohui Lam, Alexander Lu, Xinhang Suksompong, Warut |
| contents | We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for several large classes of graphs in the case of two agents -- including graphs with vertex connectivity $1$ or $2$ and complete bipartite graphs -- as well as for paths, stars, and cycles in the general case where the number of agents can be arbitrary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Welfare Loss in Connected Resource Allocation Bei, Xiaohui Lam, Alexander Lu, Xinhang Suksompong, Warut Computer Science and Game Theory Discrete Mathematics We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian welfare. Specifically, we introduce the concept of egalitarian (resp., utilitarian) price of connectivity, which captures the worst-case ratio between the optimal egalitarian (resp., utilitarian) welfare among all allocations and that among connected allocations. We provide tight or asymptotically tight bounds on the price of connectivity for several large classes of graphs in the case of two agents -- including graphs with vertex connectivity $1$ or $2$ and complete bipartite graphs -- as well as for paths, stars, and cycles in the general case where the number of agents can be arbitrary. |
| title | Welfare Loss in Connected Resource Allocation |
| topic | Computer Science and Game Theory Discrete Mathematics |
| url | https://arxiv.org/abs/2405.03467 |