## 2 Related Works
### Algorithms without Using Localization  
Algorithms without using localization do not employ full location information to select the next forwarding nodes. In this category, routing algorithms use different information and criteria than localization algorithms to identify the next forwarding nodes such as hop-count, dynamic address, physical distance, depth, and layering. Based on these criteria, algorithms without using localization are divided into two groups: bacon-based and pressure-based. Beacon-based algorithms, during the routing process, identify the next forwarding nodes using specific information such as physical distance and ID distribution. The sink node has provided this information by sending beaconing messages to the network. In the second group, pressure-based algorithms employ depth information to identify the next forwarding sensor nodes using a pressure sensor that measures the depth locally without using any beacon message. Depth information helps the sender node to identify the shallower sensors among neighbors. The following paragraphs discuss some well-known algorithms using localization. This section reviews the non-localization algorithms, which do not need full location data related to UWSNs from the sink. Authors in depth-based routing (DBR) proposed the first non-localization routing scheme [28]. Each node with a lower depth than the sender node can join the forwarding procedure; furthermore, all the nodes hold the packets for a specific time to keep the data packets. Specifically, the sensor with a lower depth becomes the shorter holding time. DBR uses depth only for forwarding the data. Consequently, each node has a smaller depth consistently included in the forwarding procedure. Thus, many nodes will die earlier than others, therefore, unbalancing the power consumption between different nodes and making routing holes (communication void) in the UWNs. Moreover, the number of repetitive transmissions grows with the rise in the network density due to the tiny variations between the nodes' depth. In terms of beacon-based techniques, in [37], the authors proposed a hop-by-hop dynamic protocol named H2-DAB as a non-localization protocol. Each sensor has a unique ID called (Hop-ID); this ID is indicated to all sensors based on hop count toward the sink node. The H2-DAB broadcasts a tiny message from the sink. The node that collects the message will get a Hop-ID. Then, the nodes will rise and broadcast a Hello message with a new Hop-ID. Each node placed near the sink will get a small Hop-ID because the Hop-ID increases with higher depth sensors. Accordingly, the sensor with a lower Hop-ID is selected to be a forwarding node. However, the H2-DAB protocol suffers from many issues such as the nodes with small Hop-ID die soon because these nodes are used continuously more than the rest nodes. Moreover, the H2-DAB applies on the matrix method that is hop count based, which is not a proper UWSN approach. Moreover, inquiry requests during the forwarding process and inquiry reply messages inundated more delay and power consumption. In [38], the authors introduced another location-free protocol based on physical distance named a reliable and energy efficient routing protocol (RERP2R). The proposed protocol is an extended form of the energy-efficient routing protocol for UWSNs [39]. The proposed approach intends to enhance the reliability between nodes, which can be done through choosing the next forwarding, depending on the link quality. Therefore, the RERP2R employs a link quality metric called a physical distance and residual energy as well as expected transmission count (ETX). RERP2R consists of three stages: initialization, packet forwarding, and, finally, the maintenance stage. In the first stage, sensor nodes exchange the residual energy between neighbors and measure the ETX along with the distance. Next, each sensor spreads these data to its neighbors. Finally, all nodes obtain information about their neighbors' residual energy, ETX, and physical distance.