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The Matching Problem in General Graphs is in Quasi-NC

Ola Svensson
École polytechnique fédérale de Lausanne
January 22, 2018

We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in polylogarithmic time on quasi-polynomially many processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani to obtain a Randomized NC algorithm.