Strong Coresets for Subspace Approximation and k-Median in Nearly Linear Time

12/27/2019

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by   Zhili Feng, et al.

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Recently the first (1+ϵ)-approximate strong coresets for k-median and subspace approximation of size poly(k/ϵ) were obtained by Sohler and Woodruff 2018. Importantly, given n points in R^d, the size of these coresets was the first that was independent of both n and d. Unfortunately their construction had a running time which was exponential in poly(k/ϵ). Here we give the first polynomial time, and in fact nearly linear time, algorithms for constructing such coresets. Our first algorithm runs in nnz(A)/ϵ + (n+d) poly(k/ϵ) time and our second runs in nd log^2(nd) + (n+d) poly(k/ϵ) time.