Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments · arXivDesk
1806.09683Jun 25, 2018An extended abstract of this work appeared at ESA '18. This version has a new coauthor (Tomohiro Koana) and an extended experimental section including comparison against two further implementations for finding matchings. Moreover, it contains further data reduction rules (theoretical and practical findings) for Maximum-Cardinality Matching and improved theoretical bounds on the kernel sizes
Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments
Tomohiro Koana, Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, Philipp Zschoche
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 O(mn)
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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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