Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
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A new algorithm finds a matroid basis in tilde O(n to the 3/7) adaptive rounds via independence oracle.
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An $\widetilde{O} (n^{3/7})$ Round Parallel Algorithm for Matroid Bases
A new algorithm finds a matroid basis in tilde O(n to the 3/7) adaptive rounds via independence oracle.