Deterministic Clustering in High Dimensional Spaces: Sketches and Approximation
precision parameter ε or k. Furthermore, there is no coreset construction that succeeds with probability 1−1/n and whose size does not depend on the number of input points, n. This has led researchers in the [...] exponential in the dimension are Ω(1) for both k-median and k-means, even when allowing a complexity FPT in the number of clusters k. This stands in sharp contrast with the (1+ε)-approximation achievable in [...] also show a deterministic algorithm for computing a (1+ε)-approximation to k-median and k-means in high dimensional Euclidean spaces in time 2^(k^2/ε^O(1)) poly(nd), close to the best randomized complexity …
