Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limitations of the Hyperplane Separation Technique for Bounding the
  Extension Complexity of Polytopes   We illustrate the limitations of the hyperplane separation bound, a
non-combinatorial lower bound on the extension complexity of a polytope. Most
notably, this bounding technique is used by Rothvo{\ss} (J ACM 64.6:41, 2017)
to establish an exponential lower bound for the perfect matching polytope. We
point out that the technique is sensitive to the particular choice of slack
matrix. For the canonical slack matrices of the spanning tree polytope and the
completion time polytope, we show that the lower bounds produced by the
hyperplane separation method are trivial. These bounds may, however, be
strengthened by normalizing rows and columns of the slack matrices.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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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: hep-ex
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The categories of this paper are: comp-gas