Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Packing Disks into Disks with Optimal Worst-Case Density   We provide a tight result for a fundamental problem arising from packing
disks into a circular container: The critical density of packing disks in a
disk is 0.5. This implies that any set of (not necessarily equal) disks of
total area $\delta\leq 1/2$ can always be packed into a disk of area 1; on the
other hand, for any $\varepsilon>0$ there are sets of disks of area
$1/2+\varepsilon$ that cannot be packed. The proof uses a careful manual
analysis, complemented by a minor automatic part that is based on interval
arithmetic. Beyond the basic mathematical importance, our result is also useful
as a blackbox lemma for the analysis of recursive packing algorithms.

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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio