A network with a static sink suffers from a severe
problem, called energy sink-hole problem, where the sensors located around the static sink are
heavily used for forwarding data to the sink on behalf of other sensors. As a result, those heavily
loaded sensors close to the sink deplete their battery power more quickly, thus disconnecting the
network. This problem exists even when the static sink is located at its optimum position
corresponding to the center of the sensor field [45]. To address this problem, a mobile sink for
gathering sensed data from source sensors was suggested [45]. In this case, the sensors
surrounding the sink change over time, giving the chance to all sensors in the network to act as
data relays to the mobile sink and thus balancing the load of data routing on all the sensors. Under
the shortest-path routing strategy, the average load of data routing is reduced when the
trajectories of the sink mobility correspond to concentric circles (assuming that the sensor field is
a circle). Another category of mobility trajectories is to move the sink in annuli. However, such
movement can be viewed as a weighted average over the movements on a set of concentric
circles. In particular, the optimum mobility strategy of the sink is a symmetric strategy in which
the trajectory of the sink is the periphery of the network. The trajectory with a radius equal to the
radius of the sensor field maximizes the distance from the sink to the centre of the network that