When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.46
URN: urn:nbn:de:0030-drops-81166
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8116/
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### The Power of Linear-Time Data Reduction for Maximum Matching

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### Abstract

Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in O(m\sqrt{n}) time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.

### BibTeX - Entry

@InProceedings{mertzios_et_al:LIPIcs:2017:8116,
author =	{George B. Mertzios and Andr{\'e} Nichterlein and Rolf Niedermeier},
title =	{{The Power of Linear-Time Data Reduction for Maximum Matching}},
booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
pages =	{46:1--46:14},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-046-0},
ISSN =	{1868-8969},
year =	{2017},
volume =	{83},
editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},