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We present a deterministic kinetic data structure for the facility location problem that maintains a subset of the moving points as facilities such that, at any point of time, the accumulated cost for the whole point set is at most a constant factor larger than the optimal cost. In our scenario, each point can change its status between client and facility and moves continuously along a known trajectory in a d-dimensional Euclidean space, where d is a constant.Our kinetic data structure requires O(n(log d (n) + log(nR))) space in total, where. . , p n } is the set of given points, and f i , d i are the maintenance cost and the demand of a point p i , respectively. In case that each trajectory can be described by a bounded degree polynomial, we process O(n 2 log 2 (nR)) events, each requiring O(log d+1 (n) · log(nR)) time and O(log(nR)) status changes.

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