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We study the problem of moving network Voronoi diagram: given a network with n nodes and E edges. Suppose there are m sites (cars, postmen, etc) moving along the network edges, we design the algorithms to compute the dynamic network Voronoi diagram as sites move such that we can answer the nearest neighbor query efficiently. Furthermore, we extend it to the k-order dynamic network Voronoi diagram such that we can answer the k nearest neighbor query efficiently. We also study the problem when the query point is allowed to move at a given speed.