The traditional problems of facility location are defined statically; a set (or multiset) of n points is given as input, corresponding to the positions of clients, and a solution is returned consisting of set of k points, corresponding to the positions of facilities, that optimizes some objective function of the input set. In the k-centre problem, the objective is to select k points for locating facilities such that the maximum distance from any client to its nearest facility is minimized. In the k-median problem, the objective is to select k points for locating facilities such that the average distance from each client to its nearest facility is minimized. A common setting for these problems is to model clients and facilities as points in Euclidean space and to measure distances between these by the Euclidean distance metric. In this thesis, we examine these problems in the mobile setting. A problem instance consists of a set of mobile clients, each following a continuous trajectory through Euclidean space under bounded velocity. The positions of the mobile Euclidean k-centre and k-median are defined as functions of the instantaneou
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