Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetry in integer lattices   The edge isoperimetric problem for a graph $G$ is to determine, for each $n$,
the minimum number of edges leaving any set of $n$ vertices. In general this
problem is NP-hard, but exact solutions are known in some special cases, for
example when $G$ is the usual integer lattice. We solve the edge isoperimetric
problem asymptotically for every Cayley graph on $\mathbb Z^d$. The
near-optimal shapes that we exhibit are zonotopes generated by line segments
corresponding to the generators of the Cayley graph.

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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg