Deterministic clustering with data nets

We consider the K-clustering problem with the `2 distortion measure, also known as the problem of optimal fixed-rate vector quantizer design. We provide a deterministic approximation algorithm which works for all dimensions d and which, given a data set of size n, computes in time poly(K)(d/ε)n log log n+(d/ε) a solution of distortion at most 1+ε times optimal. The key tool is construction of a new kind of representation called a ”data net”. A variety of applications of this object are discussed.