Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\alpha$-approximate Reductions: a Novel Source of Heuristics for Better
  Approximation Algorithms   Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a
mathematical framework for quantifying the effectiveness of preprocessing
algorithms in preserving approximation ratios. \emph{$\alpha$-approximate
reduction rules} are a central notion of this framework. We propose that
carefully crafted $\alpha$-approximate reduction rules can yield improved
approximation ratios in practice, while being easy to implement as well. This
is distinctly different from the (theoretical) purpose for which Lokshtanov et
al. designed $\alpha$-approximate Reduction Rules. As evidence in support of
this proposal we present a new 2-approximate reduction rule for the
\textsc{Dominating Set} problem. This rule, when combined with an approximation
algorithm for \textsc{Dominating Set}, yields significantly better
approximation ratios on a variety of benchmark instances as compared to the
latter algorithm alone.
  The central thesis of this work is that $\alpha$-approximate reduction rules
can be used as a tool for designing approximation algorithms which perform
better in practice. To the best of our knowledge, ours is the first exploration
of the use of $\alpha$-approximate reduction rules as a design technique for
practical approximation algorithms. We believe that this technique could be
useful in coming up with improved approximation algorithms for other
optimization problems as well.

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas