We study the problem of localizing and tracking multiple moving targets in wireless sensor networks, from a network design perspective i.e. towards estimating the least possible number of sensors to be deployed, their positions and operation characteristics needed to perform the tracking task. To avoid an expensive massive deployment, we try to take advantage of possible coverage overlaps over space and time, by introducing a novel combinatorial model that captures such overlaps. Under this model, we abstract the tracking network design problem by a combinatorial problem of covering a universe of elements by at least three sets (to ensure that each point in the network area is covered at any time by at least three sensors, and thus being localized). We then design and analyze an efficient approximate method for sensor placement and operation, that with high probability and in polynomial expected time achieves a Θ ( log n ) approximation ratio to the optimal solution. Our network design solution can be combined with alternative collaborative processing methods, to suitably fit different tracking scenarios.