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~(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) 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.
@InProceedings{korenwein_et_al:LIPIcs.ESA.2018.53, author = {Korenwein, Viatcheslav and Nichterlein, Andr\'{e} and Niedermeier, Rolf and Zschoche, Philipp}, title = {{Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments}}, booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)}, pages = {53:1--53:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-081-1}, ISSN = {1868-8969}, year = {2018}, volume = {112}, editor = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.53}, URN = {urn:nbn:de:0030-drops-95169}, doi = {10.4230/LIPIcs.ESA.2018.53}, annote = {Keywords: Maximum-cardinality matching, maximum-weight matching, linear-time algorithms, preprocessing, kernelization, parameterized complexity analysis} }
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