Measuring Connectivity Tolerance in Wireless Sensor Networks using Graph Theory Applications: A Fast Algorithm

Abstract — Wireless sensor networks today has been attracted many diverse areas in both academic and business domains because of their facility and applicability, low deployment cost and other factors. These networks aside from challenges that traditional networks have, face new challenges. These challenges can be tackled from other fields and by many tools. Since these networks can be seen from graph theory perspective as an abstract graph where sensors become nodes and links become edges in the graph, graph theory applications can be used to analyze and tackled some challenges in these networks. In this paper we first propose an exhaustive algorithm for measuring connectivity tolerance in WSNs then, since WSNs have a dynamic structure, we proposed a fast algorithm that in worst case has time complexity O(nlogn) and O(n) in normal case for measuring connectivity tolerance. Beside this parameters these algorithms can produce special data that is called meta-data, this meta-data can be used for other routing protocols or mechanisms in networks such that they do not need to run graph algorithm again, just need to operate on meta-data to obtain desire parameters. The organization of this paper is as follow, first we review the works that have been done common in both graph theory and wireless sensor networks, and in last we propose an fast algorithm for calculating connectivity tolerance for two arbitrary sensors in wireless sensor network due sensor corruption or link loss with the use of graph theory and graph mining techniques. This algorithm will test on most used sensors deployments, three sensors deployments namely, Uniform, Normal and Random distributions, then the results and conclusion will present according to these distributions. IJSE