## 2 Related Work  
Several studies have already been carried out for efficient routing protocols in UWSNs [12; 13; 14]; however, we describe the closely related work in this section, i.e., all those protocols that depend on the pipeline radius for directionality purposes using a node's relative coordinates [15] and timer information [16] for broadcasting. In [17], the authors propose Vector-Based Forwarding (VBF), which draws a fixed virtual pipeline between source and terminus point for forwarding a data packet. The forwarding decision can be made by considering the relative position of the node with reference to the pipeline. Upon reception of a data packet by a sensor node, it verifies if it is inside the virtual pipeline. If the answer is yes, then it computes the _desirableness factor_ (\(\alpha\)). The _desirableness factor_ is the ratio between the virtual pipeline width to the sum of the distance of the forwarder from the center and the source node. The forwarder nodes that are closer to the pipeline are selected each time, resulting in an energy hole in a short period of time. When the number of nodes in the network increases, it also increases the duplicate copies of the data packet due to the lesser difference between the holding time as compared to the propagation delay. Accordingly, more energy consumption occurs throughout the network and most of the packets do not reach their destination. When the network density is lower, finding a suitable node becomes more challenging. For an efficient packet delivery ratio, a single path between the terminus point and the forwarder must remain, which is indeed inflexible in VBF. To overcome the shortcomings in VBF, researchers proposed hop-by-hop VBF (HH-VBF) [18]. The HH-VBF defines a virtual pipeline on each successive forwarding hop, instead of using a single pipeline. Moreover, it improves reliability by considering pipelines to find more suitable forwarding nodes. The node transmission range is similar to that of the pipeline radius. The mechanism for calculating the timer value is similar to that of VBF. Because of the reduction in the number of void holes, the PDR is improved in HH-VBF compared to its predecessor VBF. Similar to the VBF protocol, HH-VBF can not also apply fair energy to the nodes in the network. The inadequacies of HH-VBF are covered by Adaptive HH-VBF (AHH-VBF) [19]. AHH-VBF dynamically alters the transmission power and forwarding zones. The transmission power for each forwarding data packet is enumerated to the farthest node in the transmission region and the forwarding zone is defined based on first-hop qualified nodes' density at each hop. The motivation behind the different values of the pipeline radius is to reduce the broadcasting to an acceptable level. AHH-VBF uses the _controlled packets_ to attain forwarding zone and transmission power adaptiveness. The _request packet_ is sent by the source multiple times at different transmission powers and it retains the neighbors table, while in response, it receives the _acknowledgment packet_. In this process, if the total nodes are fewer than the predefined threshold value, then the maximal power level is selected, otherwise the power level is adjusted appropriately. Adjusting the transmission power and the pipeline radius results in efficient energy tax. However, each time the same set PFNs will always be selected, which violates the fair distribution of energy among the nodes. Moreover, the dynamic power does not ensure the prevention of duplicate packets as well as the selection of qualified forwarders. Let us now consider those protocols that do not use holding time calculations, but they are based on location. The authors in [20] propose Focused Beam Routing (FBR) protocol, which uses the concept of directional power alteration in seeking directionality. Prior to forwarding packets, the source node gradually increases the flooding angle and power based on gradients defined in advance.