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German

Bibtype Inproceedings Sohler/Woodruff/2018a Sohler, Christian and Woodruff, David P. Thorup, Mikkel Strong Coresets for k-Median and Subspace Approximation: Goodbye Dimension 59th {IEEE} Annual Symposium on Foundations of Computer Science, {FOCS} 802--813 {IEEE} Computer Society We obtain the first strong coresets for the $k$-median and subspace approximation problems with sum of distances objective function, on $n$ points in $d$ dimensions, with a number of weighted points that is independent of both $n$ and $d$; namely, our coresets have size $poly(k/\eps)$. A strong coreset $(1 + \eps)$-approximates the cost function for all possible sets of centers simultaneously. We also give efficient $nnz(A)+(n+d)poly(k/\eps)+exp(poly(k/\eps))$ time algorithms for computing these coresets. We obtain the result by introducing a new dimensionality reduction technique for coresets that significantly generalizes an earlier result of Feldman, Sohler and Schmidt for squared Euclidean distances to sums of $p$-th powers of Euclidean distances for constant $p\geq 1$. 2018 SFB876-A2