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Efficient deployment strategies are proposed for a mobile sensor network, where the coverage priority of different points in the field is specified by a given function. The multiplicatively weighted Voronoi (MW-Voronoi) diagram is utilized to find the coverage holes of the network for the case where the sensing ranges of different sensors are not the same. Under the proposed strategies, each sensor detects coverage holes within its MW-Voronoi region, and then moves in a proper direction to reduce their size. Since the coverage priority of the field is not uniform, the target location of each sensor is determined based on the weights of the vertices or the points inside the corresponding MW-Voronoi region. Simulations validate the theoretical results.