## 2 Related Work  
In recent years, research on WSNs has received significant attention [9; 10; 11; 12]. Important topics discussed in the research include sensor lifetime, sensor communication performance, sensor energy consumption, and data security [13; 14; 15]. In particular, data aggregation schemes have received a lot of attention. These schemes can be divided into three general classifications: a chain-based approach, a grid-based approach, and a tree-based approach. Among chain-based data-aggregation schemes, PEGASIS [16] is the most representative. This scheme uses a greedy algorithm to connect each node to form a chain-like path. The sensors on the chain structure are randomly selected to act as the chain head, and the tail nodes at both ends of the chain structure send data to the adjacent sensors on the chain and aggregate the data, until they reach the chain head. The chain head then aggregates the detected data and sends them to the BS to complete one round of data transmission. The grid-based data aggregation scheme constructs a grid of cells in the sensing area and transmits the sensing data to the BS through the other sensor nodes. TTDD [17] is based on the grid, and the sensing area is built into a grid structure. The scheme uses a number of dissemination nodes close to the grid points responsible for storing and transmitting data. When a sensor node detects the occurrence of an event, it will become the source node (source). The sink (or BS) sends a query message through the dissemination nodes to find the source, and the source then forwards the sensing data through the dissemination nodes along the opposite direction of the query message path. DARQ [18] is an efficient data aggregation scheme in a regular area. Based on a grid structure, each sensor can obtain its location information by a global positioning system (GPS). However, when the user needs to collect information from a certain area, it will send a request message to the receiving node. After the receiver receives the request message, a data collection tree is established, and the collection area's information is gathered to the specific sensor node. Finally, the sensing data are sent to a remote receiver in a multi-hop manner. The tree-based data aggregation scheme builds a tree-like structure in the sensing area. During the data transmission, the sensor nodes transmit data along the tree structure's paths to the BS. In TBEEP [19], according to the distance between the sensor nodes and the BS, the sensing area is divided into three different tiers. [PERSON]'s algorithm is used to build a tree structure and set the path until all sensors are added to the tree. After the tree structure is established, the sensor with the highest remaining energy in the first tier is selected as the head for gathering the received data and transmitting them to the BS. During the data transmission, if all the nodes in the first tier enter a dead state, the head is selected for transmission to the second tier. This scheme will repeatedly select the head until all nodes in the tier die. In GSTEB [20], the node with the highest remaining energy is selected as the root node in the sensing area. The root node sends the collected data to the BS and each node searches for its own parent node. Next, a child node selects a parent node according to the distance of the parent node from the root node. If this distance is less than the distance between the child node and the root node, the parent node meets the selection criteria. Otherwise, the root node is selected as the parent node. For the remaining nodes not added to the tree, the previous step will be repeated to add them to the tree one after another, until all sensors are added, thus forming a tree-like structure. PEDAP [21] uses the BS as the root node and uses [PERSON]'s algorithm to establish a tree path based on the edges of the total energy consumption, until all sensors are added to the tree. In this scheme, each node has the position coordinates of all other nodes.