What question did this study set out to answer?

The aim is to explore fair allocation of indivisible items under cardinality constraints using maximin share criteria.

Maximin shares under cardinality constraints

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Demonstrates a new algorithm for fair allocation of items under constraints, suggesting improved fairness guarantees.

The aim is to explore fair allocation of indivisible items under cardinality constraints using maximin share criteria.
Developed a polynomial-time algorithm for finding approximate maximin share allocations.
Modified the algorithm for single-category instances to improve guarantees.
Extended algorithms to work with cardinality constraints.
Combined approaches with bag filling procedures.
Achieved 1/2-approximate maximin share allocations for goods, enhancing previous guarantees.
Confirmed guaranteed allocations of 2/3-approximate maximin share for single-category cases.
Established existence of allocations with a specific approximate ratio for goods and chores.

Hummel et al. (2026) studied this question.

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