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A polynomial-time algorithm for computing a Pareto optimal and almost proportional allocation
We consider fair allocation of indivisible items under additive utilities. When the utilities can be negative, the existence and complexity of an allocation that satisfies Pareto optimality and proportionality up to one item (PROP1) is an open problem. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. We point out that the result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts.
Language:
English
Keywords: polynomial algorithmfair division of goods and badsPareto frontiertrading cyclesindivisible itemsProp1
Publication based on the results of:
Мухаметшин Р. И., Скрыпник Д. В., Экономическая политика 2026 Т. 21 № 4 С. 94–109
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Added: September 27, 2026
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Added: September 25, 2026
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Added: September 25, 2026
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Added: September 25, 2026
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Added: September 25, 2026
М.: ИНФРА-М, 2026.
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