# Matching is as easy as matrix inversion

@article{Mulmuley1987MatchingIA, title={Matching is as easy as matrix inversion}, author={Ketan Mulmuley and Umesh V. Vazirani and Vijay 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.

## 767 Citations

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It is shown that a perfect matching of a line graph can be computed in NC by using a technique of dividing the graph into kingdoms, equivalent to partitioning the edge set of a graph into edge disjoint paths of even length.

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