Settling the Computational Complexity of Max-Min Allocation with Ternary Valuations

Excerpt

arXiv:2610.05237v1 Announce Type: cross Abstract: 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