A d-multi-allocation with subadditive valuations can be converted to an allocation losing only a factor of about d, yielding an Omega(1/log log n)-MMS guarantee.
Fair allocation in graphs
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From multi-allocations to allocations, with subadditive valuations
A d-multi-allocation with subadditive valuations can be converted to an allocation losing only a factor of about d, yielding an Omega(1/log log n)-MMS guarantee.