Matching is as easy as matrix inversion

@article{Mulmuley1987MatchingIA,
  title={Matching is as easy as matrix inversion},
  author={K. Mulmuley and U. Vazirani and V. Vazirani},
  journal={Combinatorica},
  year={1987},
  volume={7},
  pages={105-113}
}
We present a new algorithm for finding a maximum matching in a general graph. The special feature of our algorithm is that its only computationally non-trivial step is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorithm. At the heart of our algorithm lies a probabilistic lemma, the isolating lemma. We show other applications of this lemma to parallel computation and randomized reductions. 
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