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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2506.21493 |
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| _version_ | 1866918071338270720 |
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| author | Feige, Uriel |
| author_facet | Feige, Uriel |
| contents | We consider the problem of fair allocation of $m$ indivisible items to $n$ agents with monotone subadditive valuations. For integer $d \ge 2$, a $d$-multi-allocation is an allocation in which each item is allocated to at most $d$ different agents. We show that $d$-multi-allocations can be transformed into allocations, while not losing much more than a factor of $d$ in the value that each agent receives. One consequence of this result is that for allocation instances with equal entitlements and subadditive valuations, if $ρ$-MMS $d$-multi-allocations exist, then so do $\fracρ{4d}$-MMS allocations. Combined with recent results of Seddighin and Seddighin [EC 2025], this implies the existence of $Ω(\frac{1}{\log\log n})$-MMS allocations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From multi-allocations to allocations, with subadditive valuations Feige, Uriel Computer Science and Game Theory We consider the problem of fair allocation of $m$ indivisible items to $n$ agents with monotone subadditive valuations. For integer $d \ge 2$, a $d$-multi-allocation is an allocation in which each item is allocated to at most $d$ different agents. We show that $d$-multi-allocations can be transformed into allocations, while not losing much more than a factor of $d$ in the value that each agent receives. One consequence of this result is that for allocation instances with equal entitlements and subadditive valuations, if $ρ$-MMS $d$-multi-allocations exist, then so do $\fracρ{4d}$-MMS allocations. Combined with recent results of Seddighin and Seddighin [EC 2025], this implies the existence of $Ω(\frac{1}{\log\log n})$-MMS allocations. |
| title | From multi-allocations to allocations, with subadditive valuations |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2506.21493 |