## 1 Introduction
Additionally, the forwarding node can dynamically adjust its transmission power and prevent repeated selection of the same CH node. Ref. [16] reduced the impact of acoustic interference on data transmission by limiting the Time Division Multiple Access (TDMA) scheduling of parallel data transmission and establishes an efficient and reliable intra-cluster hierarchical route for data transmission. However, these protocols typically focus on balancing energy consumption, which may result in a low packet transmission success rate. In addition, additional network coordination may be required, such as frequent node selection or CH election. These processes can bring additional latency, which affects the need for real-time data transmission. The second category of the routing protocol prioritizes the reliability of data transmission. In [17], the protocol uses the Dijkstra algorithm to select forwarding nodes with the least neighbors to avoid collision. In [18], the directional flooding-based routing (DFR) protocol relies on packet flooding technology to improve reliability, controlling the number of nodes that flood packets and determining the number of nodes that forward them based on link quality. However, when the DFR protocol is running, the network configuration parameters are fixed, which makes it unable to deal with system changes. Consequently, the intelligent directional flooding routing (iDFR) protocol was introduced in [19], along with two new DFR versions to dynamically reflect the quality of service (QoS). The flooding area can be dynamically adjusted according to the QoS feedback provided by the sink in these protocols. These protocols prioritize the integrity of data transmission and often do not adequately consider the balance of energy consumption. For example, the DFR protocol ensures the reliability of data transmission by increasing the number of nodes participating in forwarding. However, this method increases energy consumption, particularly in densely networked scenarios. This flooding strategy may cause excessive redundant data transmissions. The first branch of the last type of routing protocol is the depth-based routing protocol, which requires only depth information. Ref. [20] introduced a depth-based routing (DBR) protocol, where the most suitable forwarding node is selected based on the maximum depth difference. Building on the work in [20], ref. [21] introduced a more lightweight depth-based routing protocol (LDBR) that considers node energy. When a node has a shallower depth and higher energy, it is more likely to participate in the routing process. In [22], the authors proposed the reliable and stability-aware routing (RSAR) protocol, aimed at reducing packet loss and improving energy efficiency. The RSAR protocol introduces a novel approach by categorizing the network into five energy levels from top to bottom, selecting the optimal forwarding node based on depth information, residual energy, and energy level. Furthermore, ref. [23] introduced a parameter called the depth threshold into the routing process and increases the consideration of the number of transmission hops, thereby ensuring the successful transmission of packets. Another branch is the location-based routing protocol. In [24], a vector-based forwarding (VBF) routing protocol was proposed, where packets are forwarded through the constructed virtual pipeline. However, the constant radius of the pipeline greatly impacts the performance of VBF. On the other hand, VBF cannot cope with the routing void phenomenon effectively. To increase the robustness and scalability of the previous protocol, the authors in [25] proposed the hop-by-hop VBF (HH-VBF) protocol, where the direction of the routing pipeline dynamically changes based on node distribution. Additionally, to reduce the impact of routing voids, ref. [26] provided its solution.