1. Formalizing Randomized Matching Algorithms
- Author
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Dai Tri Man Le and Stephen A. Cook
- Subjects
computer science - logic in computer science ,computer science - computational complexity ,mathematics - logic ,f.2.2, f.4.1 ,Logic ,BC1-199 ,Electronic computers. Computer science ,QA75.5-76.95 - 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.
- Published
- 2012
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