## 2 Previous Work  
In the realm of UASNs, there is a plethora of research to achieve efficient routing in the network [12; 13; 14]. However, here we will only focus on the specific domain of routing protocols that are related to our proposed scheme. Thus, the previous works that suppress the packet broadcast in underwater acoustic sensor networks using node location information [15] and the holding time [16], are discussed in this section. Vector based forwarding (VBF) has been proposed in [17]. VBF considers the node's location information and forwards packets through all the intermediate nodes that lie in the virtual pipeline between source and destination node pairs. When a node receives a packet from the downstream node, it first checks whether it is within the virtual pipeline or not. If a node is within the virtual pipeline, then it computes holding time using the _desirableness factor_ of the forwarder, \(\alpha\), maximum predefined delay, and the propagation delay towards the edge of the transmission range of the sender node. A desirableness factor includes the ratio of the node's distance from the center of virtual pipe and width of the virtual pipeline plus the distance from the sender node. Every time when the same sender forwards the packet, the particular set of node(s) in the neighborhood closer to the center of the virtual pipeline are penalized and die out earlier. The number of redundant packet transmissions increases when network density increases because the delay difference between their holding time becomes negligible. Accordingly, excessive energy is consumed and more packets fail to reach the Sink node. The radius of the pipeline is not fixed in the VBF. Finally, in a sparse network scenario, it is really hard to find nodes within the virtual pipeline between sender and the sink node pairs. In other words, there must exist a single path inside the virtual pipeline between sender and sink to successfully forward packet towards the sink, which is hard in the sparse network scenario. Instead of using a single virtual pipeline between sender and the Sink node, authors proposed hop-by-hop VBF (HH-VBF) [18] that forms a separate pipeline between the Sink and each forwarding or relaying hop. The authors assume that is better to form a hop-by-hop relative pipeline to find more suitable packet forwarders. The radius of the pipeline is similar to the transmission range of the node. The holding time computation in HH-VBF is not different than the VBF. HH-VBF fairly improves the packet delivery ratio compared to VBF because it increases the chance of finding more suitable forwarder within the hop-by-hop virtual pipeline. As VBF, HH-VBF fails to provide energy fairness within the network. In addition to that, HH-VBF fails to avoid any void region in the pipeline path between source and the sink node. The authors in [19], proposed Adaptive HH-VBF (AHH-VBF). It is claimed that AHH-VBF adaptively adjusts forwarding distance and the transmission power. The forwarding distance regulated base on the 1-hop neighbor density at each hop and the transmission power is computed to the maximum distant forwarder in the range. The radius of the hop-by-hop pipeline is controlled to reduce the packet forwarding by many nodes in the forwarding region. In order to achieve transmission power and forwarding area adaptiveness, AHH-VBF sends multiple _Request_ messages at different power levels and maintains the neighborhood table when it receives Acknowledgement packets in response to the _Request_. If the number of neighbors found during this process is less than \(\tau\), then transmission power is set to the maximum power; otherwise, it is adjusted accordingly. The energy efficiency is achieved through the transmission power adjustment and pipeline radius. However, several data packet transmissions from the same source node will always select the same set of forwarders, which violates the energy fairness in the network as in HH-VBF.