## 2 Related Work
For each tour distance/time is being considered as the constraint for the mobile-sink(s) and then by formulating the SHDGP problem into a mixed integer program its NP-hardness is proved. Afterward, a tour-planning heuristic is proposed. The authors claimed that their solution is suitable for large-scale networks, however, it is not practical to visit a large number of sensor-nodes one-by-one with considering distance/time constraint. To overcome the problem of direct approaches for large-scale WSNs, the idea of defining a set of sensor-nodes as Rendezvous Points (RPs) is proposed and still it is under development by considering different assumptions and employing new technologies in [9; 32; 33; 11; 34]. Generally, the mobile-sink visits the RPs instead of visiting the sensor-nodes one-by-one and other sensor-nodes will be assigned to suitable RPs that can minimize their communication range. In [32], [PERSON] et al. developed two rendezvous planning algorithm which are RP-CP and RP-UG. RP-CP attempts to determine the moving trajectory of the mobile-sink and RPs by constructing the data routing tree in the base-station. Then, the algorithm starts to find the most important edges in the tree. The importance of an edge is measured by the number of source-to-root paths from the edge. The mobile-sink starts its tour by passing from the most important edges and other sensor-nodes which are not located on the tour, transfer their data to the closest RP which is located on the tour. In this approach, the movement strategy is limited to the routing tree. However, in RP-UG the main motivation is to assume that the mobile-sink can move freely in the network. RP-UG is a utility-based greedy heuristic which improves itself by iterations. In each new iteration, the previous tour will be extended by adding new RPs to the tour until satisfying the maximum tour length. And the utility is defined as the trade-off between the mount of energy that can be saved by adding a RP and the length of the tour that is being increased. To discuss about some of the disadvantages of RP-CP and RP-UG, in RP-CP constructing the data routing tree in the base-station requires for obtaining the position of sensor-nodes which is an expensive (by considering time and energy) process in case of large-scale WSNs. And for RP-UG two practical scenarios might happen. In the first one, the base-station gathers the position of sensor-nodes and runs the algorithm which is not practical for large-scale networks. And in the second scenario the mobile-sink starts to move in the environment to determine the routes and selects the RPs which will be a time-consuming process. In [35], [PERSON] et al. studied the problem of mobility in wireless sensor networks as one of the early efforts by proposing different patterns along with data collection strategies. Their extensive numerical simulations could prove the effectiveness of employing mobile-sink in the network. In addition, in [36], [PERSON] et al. investigated the problem of applying multiple mobile-sinks in the network by identifying its characteristics. They proposed three protocols based on different degrees of network knowledge. And in [37], [PERSON] et al. provided a toolkit to simulate the application of mobile-sink in WSNs. In [9], [PERSON] et al. focused on determining the RPs and the trajectory for the mobile-sink in a distributed fashion. In the approach, the sensor-nodes with highest weight will be selected as RPs that can reduce the number of multi-hop communications in the network and conserve energy. The weight of each sensor-node will be obtained by its workload. And finally by applying the classic TSP solver, the trajectory for the mobile-sink is being calculated in the approach by considering a threshold value for tour length to guarantee data delivery delay time. In [38], [PERSON] et al. consider the problem of defining suitable trajectories for the mobile-sink by assuming the random distribution of the sensor-nodes.