Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circuit imbalance measures and linear programming   We study properties and applications of various circuit imbalance measures
associated with linear spaces. These measures describe possible ratios between
nonzero entries of support-minimal nonzero vectors of the space. The fractional
circuit imbalance measure turns out to be a crucial parameter in the context of
linear programming, and two integer variants can be used to describe
integrality properties of associated polyhedra.
  We give an overview of the properties of these measures, and survey classical
and recent applications, in particular, for linear programming algorithms with
running time dependence on the constraint matrix only, and for circuit
augmentation algorithms. We also present new bounds on the diameter and circuit
diameter of polyhedra in terms of the fractional circuit imbalance measure.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas