  Finding a maximum-cardinality or maximum-weight matching in (edge-weighted)
undirected graphs is among the most prominent problems of algorithmic graph
theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in
$\widetilde{O}(m\sqrt{n})$ time. We build on recent theoretical work focusing
on linear-time data reduction rules for finding maximum-cardinality matchings
and complement the theoretical results by presenting and analyzing (thereby
employing the kernelization methodology of parameterized complexity analysis)
new (near-)linear-time data reduction rules for both the unweighted and the
positive-integer-weighted case. Moreover, we experimentally demonstrate that
these data reduction rules provide significant speedups of the state-of-the art
implementations for computing matchings in real-world graphs: the average
speedup factor is 4.7 in the unweighted case and 12.72 in the weighted case.
