# From multi-allocations to allocations, with subadditive valuations

arXiv: https://arxiv.org/abs/2506.21493 · HTML: https://mlsanity.com/paper/2506.21493/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [EFX Allocation In (Multi)Hypergraphs](https://mlsanity.com/paper/2608.03171/) (2026)

## Abstract (arXiv)

We consider the problem of fair allocation of m indivisible items to n agents with monotone subadditive valuations. For integer d ≥ 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 fracρ4d-MMS allocations. Combined with recent results of Seddighin and Seddighin [EC 2025], this implies the existence of Omega(frac1loglog n)-MMS allocations.