# Efficient Mobile Sink Routing in Wireless Sensor Networks Using Bipartite Graphs
## 1 Introduction  
Wireless sensor networks (W.S.N.s) encounter issues when deployed to support applications requiring mobility support, such as disaster and earthquake recovery, combat field surveillance, monitoring animals, and law enforcement applications. W.S.N.s also have applications incorporating 5G internet IoT systems for psychoacoustic monitoring. As a result, to ensure reliable communication, dependable connectivity of the network, low energy usage, and prolonged network life span for these applications, a dynamic and adaptive W.S.N. network with mobility support is required [1, 2]. Consequently, these networks must preserve fault tolerance and self-organizing capabilities to operate properly [3, 4, 5, 6]. Therefore, it is vital to provide energy-efficient systems throughout the whole protocol, and stack variances in mobility play a major role and directly impact the scalability and energy efficiency of W.S.N.s. Thus, performance deterioration and unpredictably broken links result from needing to provide a reliable mobility model [1, 7, 8]. Various mobility models were proposed in the literature and are considered good candidates to be used in ad hoc networks. However, when using them in W.S.N.s, they provide low QoS parameters and increase energy consumption because they behave in these networks. In other words, sensor networks can provide different data types, such as videos. As a result, certain QoS parameters, such as bitstream, must be maintained. It is worth noting that QoS in W.S.N.s is divided into two categories: application and network dependent, such as node reading, coverage, deployment, and the number of live nodes. On the other hand, the second category is more concerned with efficiently using the bandwidth, energy consumption, throughput, and packet delivery ratio. To elaborate, the random waypoint mobility model performs reasonably when used in ad hoc networks. However, it is not a suitable choice in W.S.N.s because of its poor choice of velocity and uniform distribution [9; 10; 11; 12; 13]. On the other hand, the nomadic community mobility model was introduced to address the drawbacks of the random waypoint mobility model. Because nodes move randomly from one site to another, this model is appropriate for applications supporting military operations and mobile communications in conferences. Furthermore, based on the collective motion of the group, a reference point for each point is determined. This approach consumes much energy to discover or pinpoint the location of a single node [14; 15]. Consequently, a geographic-based circular mobility model was introduced to handle sink node mobility. This model collects data by traveling over a circular, static point-based track. The condition that nodes stay stationary eight or sixteen times during each cycle is a significant drawback in this model. Therefore, a wind mobility model based on eight directions was proposed in [14] to extend the network lifetime. This paradigm is depicted for sink nodes, although nodes in this model only support group mobility. As a result, to determine the position of one node, a group of nodes moves and consume energy [15]. Thus, the wind mobility model must provide high performance for the network due to the additional pause time, the speed of nodes, and their interdependencies [16]. Additionally, processing, sensing, and communication are the three subsystems of sensor nodes. The communication subsystem is also the main source of energy consumption because the distance between the source and destination nodes determines how much energy is used to convey a message [17; 18]. Thus, multi-hop communication can reduce the distance required in transmission, which comes at the expense of increasing the delay compared to single-hop communication [17; 19]. Furthermore, the communication between sensor nodes is accomplished according to the IEEE 802.15.4 standard, keeping in mind that the communication range depends on the sensor node's energy. Still, usually, it is less than 100 m [20].