Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The visible perimeter of an arrangement of disks   Given a collection of n opaque unit disks in the plane, we want to find a
stacking order for them that maximizes their visible perimeter---the total
length of all pieces of their boundaries visible from above. We prove that if
the centers of the disks form a dense point set, i.e., the ratio of their
maximum to their minimum distance is O(n^1/2), then there is a stacking order
for which the visible perimeter is Omega(n^2/3). We also show that this bound
cannot be improved in the case of a sufficiently small n^1/2 by n^1/2 uniform
grid. On the other hand, if the set of centers is dense and the maximum
distance between them is small, then the visible perimeter is O(n^3/4) with
respect to any stacking order. This latter bound cannot be improved either.
Finally, we address the case where no more than c disks can have a point in
common. These results partially answer some questions of Cabello, Haverkort,
van Kreveld, and Speckmann.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex