Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation Schemes for Subset Sum Ratio Problems   We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of
integers the goal is to find two subsets such that the ratio of their sums is
as close to~1 as possible, and introduce a family of variations that capture
additional meaningful requirements. Our main contribution is a generic
framework that yields fully polynomial time approximation schemes (FPTAS) for
problems in this family that meet certain conditions. We use our framework to
design explicit FPTASs for two such problems, namely Two-Set Subset-Sum Ratio
and Factor-$r$ Subset-Sum Ratio, with running time
$\mathcal{O}(n^4/\varepsilon)$, which coincides with the best known running
time for the original $SSR$ problem [15].

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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: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math
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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: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex