Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Keep Your Distance: Land Division With Separation   This paper is part of an ongoing endeavor to bring the theory of fair
division closer to practice by handling requirements from real-life
applications. We focus on two requirements originating from the division of
land estates: (1) each agent should receive a plot of a usable geometric shape,
and (2) plots of different agents must be physically separated. With these
requirements, the classic fairness notion of proportionality is impractical,
since it may be impossible to attain any multiplicative approximation of it. In
contrast, the ordinal maximin share approximation, introduced by Budish in
2011, provides meaningful fairness guarantees. We prove upper and lower bounds
on achievable maximin share guarantees when the usable shapes are squares, fat
rectangles, or arbitrary axes-aligned rectangles, and explore the algorithmic
and query complexity of finding fair partitions in this setting.

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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol