Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation by Lexicographically Maximal Solutions in Matching and
  Matroid Intersection Problems   We study how good a lexicographically maximal solution is in the weighted
matching and matroid intersection problems. A solution is lexicographically
maximal if it takes as many heaviest elements as possible, and subject to this,
it takes as many second heaviest elements as possible, and so on. If the
distinct weight values are sufficiently dispersed, e.g., the minimum ratio of
two distinct weight values is at least the ground set size, then the
lexicographical maximality and the usual weighted optimality are equivalent. We
show that the threshold of the ratio for this equivalence to hold is exactly
$2$. Furthermore, we prove that if the ratio is less than $2$, say $\alpha$,
then a lexicographically maximal solution achieves $(\alpha/2)$-approximation,
and this bound is tight.

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The categories of this paper are: nlin
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The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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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: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin