Finding a Maximum Matching in a Sparse Random Graph in O(n) Expected Time

Authors:
Prasad Chebolu;Alan Frieze;Páll Melsted
Affiliations:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A. PA15213;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A. PA15213;Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A. PA15213
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Year:
2008

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Parallel greedy graph matching using an edge partitioning approach

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Abstract

We present a linear expected time algorithm for finding maximum cardinality matchings in sparse random graphs. This is optimal and improves on previous results by a logarithmic factor.