# An Efficient Model-Based Clustering via Joint Multiple Sink Placement for WSNs
## 2 Related Works
### Data Transmission and Routing Paths  
The crucial role of each sensor in a WSN is to regularly transfer its perceived data to the sink. The simple method is Direct Transmission (DT) [34], a scheme where sensors transmit directly to the sink nodes without using an intermediate node. This configuration is mainly employed in networks with topologies that rely on a central node to oversee the operation. However, it results in an unequal depletion of energy among the nodes. As a result, nodes located far away from the sink are depleted more rapidly than nodes placed near to the sink. The significant variance in node energy consumption shortens the total network lifetime, breaching fundamental WSN requirements (energy efficiency). Several methods have been offered to address these concerns, including minimizing the energy consumption  
of SNs and enhancing their lifetime. The routing solutions may be classified into flat and hierarchical protocols. Flat routing protocols [53], such as DD [54] and SPIN [55], use data diffusion to load the network with a massive number of packets, which impacts transmission time and the network's lifetime. Flooding is the most fundamental adaptive strategy for WSNs. It is highly dependable since it ensures network throughput across the sink's many little paths. However, it suffers from traffic implosion, overlapping, and resource blindness [56]. Clustering techniques are used in hierarchical routing to improve network performance. Clusters of nodes are formed, with each cluster having its own head node. The Cluster Head nodes are in charge of gathering and aggregating data from the particular clusters and relaying the aggregated data to the sink node. Low energy adaptive clustering hierarchy (LEACH) [57], power-efficient gathering in sensor information systems (PEGASIS) [36], centralized energy efficient distance (CEED) [31], threshold-sensitive energy efficient sensor network protocol (TEEN) [58] and general self-organized tree-based energy-balance (GSTEB) [37] are some of the most well-known hierarchical routing systems. One of the first studies on this issue was in relation to the LEACH system. In this system, the CH receives data from the other members' nodes in the cluster, collects it, and then sends it all to a base station. LEACH rotates the CH to ensure that energy usage is evenly distributed. The dynamic and distributed clustering protocol LEACH is the most outstanding example. LEACH increases the network lifetime by eight times more than DT. Nonetheless, it assumes that the medium is static. In another way, several solutions to improve network lifetime using the Compressive Sensing (CS) theory have been proposed by researchers. Cluster-based routing, CS theory and single-sink deployment are all discussed in [59]. The researchers evaluated the influence of BS location on transmission numbers and offered two data gathering approaches: Energy-aware CS-based Data Aggregation and Energy-balanced High level Data aggregation Tree (EHDT). The distance between nodes and the associated sink is a critical factor in choosing the best path to transmit the collected data in an energy-efficient routing technique [38]. This low-energy routing path should in fact reduce communication costs. Using block-diagonal matrices as measurement matrices, ref. [60] combined CDG and clustering in WSNs, resulting in a significant decrease in transmission power utilization. These cluster-based CDG methods, however, still necessitate a substantial amount of intra-cluster data exchanges. Furthermore, none of the previous studies have looked into the robustness of signal recovery performance in the event of network node drops. The authors of [33] presented two algorithms: Multi-sink Placement and Anycast Routing (MPAR), and Extended Multi-sink Placement and Anycast Routing (EMPAR). The two algorithms are built for a two-level architecture, with nodes grouped on the first level. A load-balanced data aggregation routing tree connects SNs to the corresponding CH.