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The power of linear-time data reduction for matching.

Mertzios, G.B. and Nichterlein, A. and Niedermeier, R. (2017) 'The power of linear-time data reduction for matching.', in 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) : August 21-25, 2017, Aalborg (Denmark) ; proceedings. Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, p. 46. LIPIcs–Leibniz International Proceedings in Informatics. (83).


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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution.
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Publisher statement:© George B. Mertzios, André Nichterlein, Rolf Niedermeier; licensed under Creative Commons License CC-BY
Date accepted:12 June 2017
Date deposited:28 June 2017
Date of first online publication:01 November 2017
Date first made open access:No date available

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