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

Authors Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, Philipp Zschoche

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Viatcheslav Korenwein
  • TU Berlin, Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany
André Nichterlein
  • TU Berlin, Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany
Rolf Niedermeier
  • TU Berlin, Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany
Philipp Zschoche
  • TU Berlin, Institut für Softwaretechnik und Theoretische Informatik, Berlin, Germany

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Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche. Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 53:1-53:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ESA.2018.53

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 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Maximum-cardinality matching
  • maximum-weight matching
  • linear-time algorithms
  • preprocessing
  • kernelization
  • parameterized complexity analysis

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