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VOLUME 8, ISSUE 3, PAPER 5


Formalizing Randomized Matching Algorithms

©Dai Tri Man Le, University of Toronto
©Stephen A. Cook, University of Toronto

Abstract
Using Jev{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.

Publication date: August 10, 2012

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-8(3:5)2012

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