The MDEA model admits tight 1/ℓ-approximations for simultaneous USW and ESW efficiency across ℓ dimensions with NP-hardness for exact simultaneous optimization even with binary valuations, plus characterizations of three multidimensional Pareto notions.
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Abbottet al., Physical Review D99(2019), 10.1103/physrevd.99.123505
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Simultaneously Efficient Allocation of Indivisible Items Across Multiple Dimensions
The MDEA model admits tight 1/ℓ-approximations for simultaneous USW and ESW efficiency across ℓ dimensions with NP-hardness for exact simultaneous optimization even with binary valuations, plus characterizations of three multidimensional Pareto notions.