# Energy and Distance-Aware Hopping Sensor
## 1 Introduction  
Big data includes comprehensive technologies which analyze and add values to a large amount of data. Novel techniques for collecting and transmitting data have become very important along with the advance of big data technology [1]. Therefore, networking between sensor nodes plays a great role in progressing big data industry [2; 3]. Several decades have witnessed the dramatic rise of wireless sensor network technology to exploit environment, weather, and battle field information. A wireless sensor network has a wide variety of applications under radioactive contaminated regions, battle fields, and/or a region of disaster [4; 5]. It is very hard to approach these regions due to harmful chemicals or unavoidable obstacles. Moreover, hundreds of sensors deployed in an enemy site gathers a lot of valuable military information. The scattering of the sensors through wide and rough surfaces is of critical importance to collect valuable data especially in unmanned area. However, the small-sized sensors have a limitation of energy due to the small volume of battery capacity. Some sensors consume their energy quicker than other nodes due to an uneven access to those sensors. In the worst case, the communication between sensors might shut down due to an energy-depletion of only a few nodes. To avoid the unexpected shutting down of the whole network, several energy-efficient schemes have been proposed. Rerouting or multipath by load-balancing are some noticeable schemes in this direction of research [6; 7; 8]. A region which is not covered by a data-collecting sensor node is called a \"sensing hole\". That is, as the number of faulty sensors increases, sensing holes emerge [9]. The main reason of this sensor death is power depletion. Several schemes have been proposed to prevent the appearance of sensing holes. These schemes include sensor state (active/idle) control and efficient path routing. Mobile sensors are able to approach dangerous area autonomously and replace dead sensor nodes. Initial studies for the mobile sensors were just focusing on the sensor relocation capability. In this scheme, fixed sensors scattered in a Wireless Sensor Networks (WSN) region are responsible for guiding mobile sensors to the wanted directions. Reference [10] demonstrates a mobile network structure in which wheeled mobile devices replace malfunctioned fixed nodes. However, the wheel-based movement is not suitable for rugged surfaces which prevent fast deployment, hence it leads to a quick power consumption. Hopping-based relocation is proposed to overcome the limitation of the wheel-based scheme. A hopping sensor node is designed to jump to a specific direction which can be steered by the users. Reference [11] demonstrates some specifications of the jumping robots, as shown in Figure 1, including the maximum height and operational range. For another example, the mobile unit, as shown in Figure 1, funded by DARPA is able to reach a maximum 10-m height and hop 100 times with one fuel injection [12; 13]. Sensor relocation to recover sensing holes by mobile sensors has attracted many researchers. The authors of Reference [14] propose a sensor relocation scheme based on the shortest path manner. However, specific sensors on the shortest path are frequently accessed, and thus additional sensing holes can be generated by these sensors. To remedy this problem, Reference [15] proposes a multipath scheme instead of the single shortest path policy. Reference [15] lowers the uneven movement of hopping sensors which causes a fast energy exhaustion of specific sensors. Reference [15] also improves the ratio of operational hopping sensors in the network as well as the success ratio of sensor relocation, compared to the shorted path method. The sensing holes arise randomly, and the appearance of them is not limited to the specific region. It is also possible that multiple holes arise simultaneously. A repetition of the shortest path relocation can be used to cover multiple sensing holes.