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We study the problem of fair allocation of a set of indivisible items among agents with additive valuations, under cardinality constraints. In this setting, the items are partitioned into categories, each with its own limit on the number of items it may contribute to any bundle. We consider the fairness measure known as the maximin share (MMS) guarantee, and propose a novel polynomial-time algorithm for finding 1/2-approximate MMS allocations---an improvement from the previously best available guarantee of 11/30.
Hummel et al. (Mon,) studied this question.