Sparse convex hull coverage

Given a set P of n data points and an integer k, fundamental computational task is to find smaller subset Q⊆P only k which approximately preserves the geometry P. Here we consider problem finding Q best captures convex hull P, where our error measure sum distances in Q. We generalize allow R that must select from differ as well more general functions uncovered such other norms or weighted distance functions. prove approximating this manner plane can be solved by either simple graph based dynamic programming algorithm polynomial time. Complementing result show three dimensions higher NP-hard. Moreover, give selects O(klog⁡(n/ε)) get solution whose at most 1+ε times optimal point error. This generalizes O(k⌊d/2⌋log⁡(n/ε)) for any constant dimension d.