Matching is as easy as matrix inversion

Abstract

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. © 1987 Akadémiai Kiadó.