eps-Kernel Coresets for Stochastic Points

7 We study the problem of constructing ε-kernel coresets for uncertain points. We consider uncertainty8under the existential model where each point’s location is fixed but only occurs with a certain probability,9and the locational model where each point has a probability distribution describing its location. An ε-10kernel coreset approximates the width of a point set in any direction. We consider approximating the11expected width (an ε-exp-kernel) and the probability distribution on the width (an ε-quant-kernel) for12any direction. We provide a near-linear time algorithm to construct a set of O(1/ε(d−1)/2) deterministic13points which approximate the expected width under the existential and locational models. We show in14general it is not possible to provide a subset of the original uncertain points which provides such an15approximation. However, if the existential probability of each point is lower bounded by a constant, an16ε-exp-kernel is still possible. We also construct an ε-quant-kernel coreset under the existential model.17