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

Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, Philipp Zschoche, Michael Wagner
2018 European Symposium on Algorithms  
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 medge graphs, the best known algorithms run in O(m √ 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
more » ... exity analysis) linear-time data reduction rules for the positive-integer-weighted case. Moreover, we experimentally demonstrate that these data reduction rules provide significant speedups of the state-of-the art implementation for computing matchings in real-world graphs: the average speedup is 3800% in the unweighted case and "just" 30% in the weighted case.
doi:10.4230/lipics.esa.2018.53 dblp:conf/esa/KorenweinNNZ18 fatcat:3oouhvueibbgtplx24rmqdgvw4