Industry 4.0 utilizes the Internet of Things (IoT) to rise the efficiency in manufacturing and automation where wireless sensor networks (WSNs) are crucial technologies for communication layer of IoT. WSNs include hundreds of small sized sensor nodes that have the abilities of wireless transmission and environmental sensing. Wireless transmission is prone to various attacks such as data manipulation since data communication is achieved through transfer of radio packets. A countermeasure of this issue is link monitoring by deploying secure points that can physically capture and inspect radio packets. Graph theory plays a critical role to solve various problems in WSNs. Finding minimum Vertex Cover (VC) is an important NP-Hard graph theoretic problem in which the minimum set of nodes (vertices) is aimed to select in such a way that each link should be incident to at least one node from this set. VC is a significant structure for WSNs where it perfectly fits for link monitoring when nodes in VC are set as secure points (monitors). Since sensor nodes are generally battery-powered and have limited transmission range, energy-efficient multi-hop communication to the sink node is of utmost importance. In weighted connected VC (WCVC) structure, subgraph induced by monitor nodes are connected where monitors are chosen according to their weights. When weights of nodes are assigned as reciprocal of their energies, an energy-efficient virtual backbone can be formed. We propose a novel metaheuristic WCVC algorithm for link monitoring and backbone formation in WSNs modeled as undirected graphs. Our proposed algorithm integrates a genetic search with a greedy heuristic to improve WCVC solution quality and decrease the search time. To evaluate the efficiencies of greedy heuristics, we adopt three different heuristics for WCVC problem. We implement our algorithm with its counterparts and reveal that the algorithm is favorable in terms of solution quality and resource consumption.

A Wireless Sensor Network (WSN) is connected if a communication path exists among each pair of sensor nodes (motes). Maintaining reliable connectivity in WSNs is a complicated task, since any failure in the nodes can cause the data transmission paths to break. In a k-connected WSN, the connectivity survives after failure in any k-1 nodes; hence, preserving the k-connectivity ensures that the WSN can permit k-1 node failures without wasting the connectivity. Higher k values will increase the reliability of a WSN against node failures. We propose a simple and efficient algorithm (PINC) to accomplish movement-based k-connectivity restoration that divides the nodes into the critical, which are the nodes whose failure reduces k, and non-critical groups. The PINC algorithm pickups and moves the non-critical nodes when a critical node stops working. This algorithm moves a non-critical node with minimum movement cost to the position of the failed mote. The measurements obtained from the testbed of real IRIS motes and Kobuki robots, along with extensive simulations, revealed that the PINC restores the k-connectivity by generating optimum movements faster than its competitors.

k-connectivity is a strong notion of robust connectivity. Indeed, in a k-connected network each node has k disjoint paths to all the other nodes in the network. Therefore, even in the case of k-1 node/link failure(s), a k-connected wireless sensor network (WSN) remains connected because each node still has, at least, one path to the rest of the surviving nodes. Networks with higher k values are, typically, more reliable and fault tolerant than those with lower k values. In this study, we present a systematic and dedicated overview of WSN k-connectivity problem. We, first, outline the k-connectivity detection problem (i.e., determining the k value of a network). Second, we explore the k-connected network deployment problem. Third, we dissect the restoration problem that addresses the rehabilitation of a deteriorated network to restore its original k value. Built upon the provided foundations, we identify and discuss a rich set of important and promising open research problems along with pointers to possible solution approaches.