For every n≥4 there are tri-valued additive chore instances with no EFX allocation, bi-valued instances where every EFX allocation fails Pareto optimality, and EFX is guaranteed for four bi-valued agents.
A Proof of Theorem 1 for Generaln In this section, we prove Theorem 1 for an arbitrary fixedn≥4
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Simpler poly-time constructions for EF2X/EF3X and improved √2/2-EFX and 2/3-EFX approximations for monotone and additive valuations in restricted hypergraphs.
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Almost EFX in Hypergraphs
Simpler poly-time constructions for EF2X/EF3X and improved √2/2-EFX and 2/3-EFX approximations for monotone and additive valuations in restricted hypergraphs.