For mixed goods and chores, a weighted Pareto-optimal allocation that is proportional up to one item always exists and is computable in strongly polynomial time.
Efficient re alloca- tion under additive and ordinal preferences
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A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation
For mixed goods and chores, a weighted Pareto-optimal allocation that is proportional up to one item always exists and is computable in strongly polynomial time.