A network recovery strategy based on boundary nodes and tetrahedral approximation fermat points in three-dimensional wireless sensor networks.

Wireless Sensor Networks (WSNs) have emerged as a critical research frontier in the Internet of Things (IoT) domain, with widespread applications in three-dimensional environments. However, due to harsh environments (such as high temperature, high pressure, etc.), natural disasters (such as earthquakes, etc.), large-scale attacks (such as bombing), WSNs in a certain area is split into many isolated islands, and the regional network fails. In emergency scenarios, restoring network connectivity in a timely manner is essential for ensuring reliable data transmission. However, finding the minimum relay node to recover the network is an NP hard problem. To address this challenge, this paper proposes a novel connectivity recovery strategy for 3D wireless sensor networks by leveraging boundary nodes and tetrahedral approximate Fermat points. The proposed approach is evaluated through three distinct algorithms: (1) a variant of Prim's algorithm (VPrim), which iteratively connects pairs of isolated segments until full network connectivity is restored, (2) a tetrahedral approximate Fermat point algorithm (TAFP), which simultaneously connects four isolated segments in each iteration until the network is fully recovered, and (3) Hybrid TAFP and VPrim Algorithm (HybridTV) to restore the entire network. Extensive simulation experiments demonstrate that our strategy significantly reduces the number of required relay nodes, enhances connectivity in the recovered network topology, and improves overall fault tolerance, offering a robust solution for network recovery in complex 3D environments.