Before revision:  We also give a randomized online algorithm with competitive ratio O(d^2) for Unit Clustering of integer points (i.e., points in Z^d, d\in N, under L_{\infty} norm)  .
After revision:  We also give a randomized online algorithm with competitive ratio O(d^2) for Unit Clustering of integer points (i.e., points in Z^d, d\in N, under L_{\infty} norm) . We show that the competitive ratio of any deterministic online algorithm for Unit Covering is at least 2^d. This ratio is the best possible, as it can be attained by a simple deterministic algorithm that assigns points to a predefined set of unit cubes .