The Matching Problem in General Graphs Is in Quasi-NC

@article{Svensson2017TheMP,
  title={The Matching Problem in General Graphs Is in Quasi-NC},
  author={Ola Svensson and Jakub Tarnawski},
  journal={2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)},
  year={2017},
  pages={696-707}
}
  • O. Svensson, Jakub Tarnawski
  • Published 6 April 2017
  • Mathematics, Computer Science
  • 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
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 O(\log^3 n) time on n^{O(\log^2 n)} 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 [1987] to obtain a Randomized NC algorithm.Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who proved the analogous… 
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