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The Power of Linear-Time Data Reduction for Maximum Matching

André Nichterlein (TU Berlin)

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.



André Nichterlein
TEL 512

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