Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Generalized Independent and Dominating Set Problems on Unit Disk
  Graphs   In this article, we study a generalized version of the maximum independent
set and minimum dominating set problems, namely, the maximum $d$-distance
independent set problem and the minimum $d$-distance dominating set problem on
unit disk graphs for a positive integer $d>0$. We first show that the maximum
$d$-distance independent set problem and the minimum $d$-distance dominating
set problem belongs to NP-hard class. Next, we propose a simple polynomial-time
constant-factor approximation algorithms and PTAS for both the problems.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
12
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: patt-sol
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The categories of this paper are: math