For arbitrary n agents, a Pareto-optimal category-constrained allocation always exists such that envy-freeness holds after reallocating at most min{k+1,n}(n-1) items per agent, computable in polynomial time for constant n via a new KKM-lemma application.
On f air division under heterogeneous matroid constraints
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Fair and efficient allocation of indivisible items under category constraints
For arbitrary n agents, a Pareto-optimal category-constrained allocation always exists such that envy-freeness holds after reallocating at most min{k+1,n}(n-1) items per agent, computable in polynomial time for constant n via a new KKM-lemma application.