Modified Floyd–Warshall’s Algorithm for Maximum Connectivity in Wireless Sensor Networks under Uncertainty

Abstract

The main objective of this paper is to find the duration of maximum time connectivity of sensor nodes under uncertainty utilizing the prespecified voltage/power of each sensor node. Wireless sensor networks (WSNs) are composed of nodes that transmit data between each other over routing. A variety of routing protocols and algorithms exist, each related to a particular set of conditions. There are a variety of routing algorithms available, some of which can be used in WSNs for routing. The goal of the fastest distance routing algorithms in a WSN is to use the least amount of energy possible. In a WSN, Dijkstra’s algorithm is typically used for shortest path routing. The Floyd–Warshall’s algorithm is used to compute the shortest paths between distinct nodes in a regular graph, but due to the absence of a communication mode, this algorithm is not ideal for routing in wireless networks. In this research work, we have considered a WSN to find out the maximum connectivity time utilizing optimum voltage. On the other hand, duration of connectivity and energy/voltage are two vital parameters that are difficult to manage. Because of limited resources and safety concerns, safety implementation is limited. Also, due to the irregular/hazardous environmental situations, the distance between sensor nodes and its voltage to link up the nodes are totally unpredictable. In this work, we employ triangular fuzzy numbers to express unpredictability. Then, utilizing defuzzification of fuzzy numbers, the associated WSN problem was transformed into a crisp one. The widely used signed distance approach has been applied for the defuzzification of fuzzy numbers in this case. To determine the best outcome and to illustrate the usefulness of the suggested technique, a numerical example has been solved using the modified Floyd–Warshall’s algorithm. Finally, concluding remarks on the proposed approach as well as future studies have been provided.

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