Settling the Computational Complexity of Max-Min Allocation with Ternary Valuations
We study the problem of computing an allocation of indivisible items that maximizes egalitarian welfare, i.e., the utility of the worst-off agent, when agents' item values or marginal values belong to a small set. For additive valuations with values in $\{p,q\}$, where $q>p>0$ and $\gcd(p,q)=1$, we give a polynomial-time algorithm when $p=2$ and prove constant-gap hardness when $p\geq3$, already with exactly three high-valued goods per agent. We also give an $\sqrt{3/2}$-approximation for common positive bi-valued additive valuations. For mixed additive valuations in $\{-p,0,c\}$, where $p\in\{1,2\}$ and $c$ is a positive integer, a reduction to maximum-weight perfect matching resolves th...
| Authors | Thi Ngoc Anh Vu, Trung Thanh Nguyen, Khaled Elbassioni et al. |
|---|---|
| Primary category | cs.GT |
| Published | 4 October 2026 |
| Last updated at source | 4 October 2026 |
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