Formalizing Randomized Matching Algorithms
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2012-08-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/973/pdf |
| Summary: | 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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| ISSN: | 1860-5974 |