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 uniform sample of size O(ε^{-2} log 1/ε) is a stable (ε, O(ε))-coreset for the geometric median with high probability, tight up to the log factor.
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A Near-Optimal Parallel Algorithm for Finding Matroid Bases
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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Optimal Stable Coresets for Geometric Median via Uniform Sampling
A uniform sample of size O(ε^{-2} log 1/ε) is a stable (ε, O(ε))-coreset for the geometric median with high probability, tight up to the log factor.