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arXiv · 1806.09683

Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments

Tomohiro Koana·Viatcheslav Korenwein·André Nichterlein·Rolf Niedermeier·Philipp Zschoche
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Abstract

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.

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Tomohiro Koana, Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, Philipp Zschoche. 2018-06-25. Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments. https://arxiv.org/abs/1806.09683

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