Formalizing Randomized Matching Algorithms
Logic in Computer Science
2015-07-01 v7 Computational Complexity
Logic
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.
Cite
@article{arxiv.1103.5215,
title = {Formalizing Randomized Matching Algorithms},
author = {Dai Tri Man Le and Stephen A. Cook},
journal= {arXiv preprint arXiv:1103.5215},
year = {2015}
}