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arXiv · 1103.5215

Formalizing Randomized Matching Algorithms

Dai Tri Man Le·Stephen A. Cook
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Abstract

Using Je\v{r}\'abek 's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC^2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning. The first algorithm is for testing if a bipartite graph has a perfect matching, and is based on the Schwartz-Zippel Lemma for polynomial identity testing applied to the Edmonds polynomial of the graph. The second algorithm, due to Mulmuley, Vazirani and Vazirani, is for finding a perfect matching, where the key ingredient of this algorithm is the Isolating Lemma.

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Dai Tri Man Le, Stephen A. Cook. 2011-03-27. Formalizing Randomized Matching Algorithms. https://doi.org/10.2168/lmcs-8(3%3A5)2012

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