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Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as amathematical framework for quantifying the effectiveness of preprocessingalgorithms in preserving approximation ratios. \emph{$\alpha$-approximatereduction rules} are a central notion of this framework. We propose thatcarefully crafted $\alpha$-approximate reduction rules can yield improvedapproximation ratios in practice, while being easy to implement as well. Thisis distinctly different from the (theoretical) purpose for which Lokshtanov etal. designed $\alpha$-approximate Reduction Rules. As evidence in support ofthis proposal we present a new 2-approximate reduction rule for the\textsc{Dominating Set} problem. This rule, when combined with an approximationalgorithm for \textsc{Dominating Set}, yields significantly betterapproximation ratios on a variety of benchmark instances as compared to thelatter algorithm alone.  The central thesis of this work is that $\alpha$-approximate reduction rulescan be used as a tool for designing approximation algorithms which performbetter in practice. To the best of our knowledge, ours is the first explorationof the use of $\alpha$-approximate reduction rules as a design technique forpractical approximation algorithms. We believe that this technique could beuseful in coming up with improved approximation algorithms for otheroptimization problems as well.

$\alpha$-approximate Reductions: a Novel Source of Heuristics for Better Approximation Algorithms