Algorithms for Finding Vulnerabilities and Deploying Additional Sensors in a Region with Obstacles

Kibeom Kim,Sunggu Lee

doi:10.3390/electronics10121504

Abstract

Consider a two-dimensional rectangular region guarded by a set of sensors, which may be smart networked surveillance cameras or simpler sensor devices. In order to evaluate the level of security provided by these sensors, it is useful to find and evaluate the path with the lowest level of exposure to the sensors. Then, if desired, additional sensors can be placed at strategic locations to increase the level of security provided. General forms of these two problems are presented in this paper. Next, the minimum exposure path is found by first using the sensing limits of the sensors to compute an approximate “feasible area” of interest, and then using a grid within this feasible area to search for the minimum exposure path in a systematic manner. Two algorithms are presented for the minimum exposure path problem, and an additional subsequently executed algorithm is proposed for sensor deployment. The proposed algorithms are shown to require significantly lower computational complexity than previous methods, with the fastest proposed algorithm requiring O(n2.5) time, as compared to O(mn3) for a traditional grid-based search method, where n is the number of sensors, m is the number of obstacles, and certain assumptions are made on the parameter values.

Highlights

A wireless sensor network (WSN) can be used for various tasks such as monitoring the environment and industrial facilities
An important application of sensor networks and WSNs is surveillance [1], which can be conducted using smart networked surveillance cameras or simple sensor devices. For this type of application, the degree of security provided by the WSN is determined mainly by the positioning of the sensors
The Voronoi diagram and Delaunay triangulation are useful concepts, they are found to be insufficient for the computation of the exact minimum exposure paths when the combined effect of multiple sensors are considered

Summary

Introduction

A wireless sensor network (WSN) can be used for various tasks such as monitoring the environment and industrial facilities. Meguerdichian et al [13,14] suggest an approach that applies a geometrical algorithm to the coverage problem They assume all n sensors are modeled with identical disks in which the sensitivity decreases as the distance between a point and a sensor increases. They set the weight of an edge in the Voronoi diagram to be the distance between that edge and the nearest sensor They find the maximal breach path using a binary search process. The number of vertices |V| and edges |E| in the Voronoi diagram are O(n), so a shortest-path search algorithm, such as Dijkstra’s algorithm, could be used to compute the maximal breach path in time O(|V|2) or O(|E| + |V| log |V|) time using a min-priority queue implemented by a Fibonacci heap [16]. The overall time complexity for the computation of the maximal breach path using a Voronoi diagram is O(n log n)

Effect of Multiple Sensors Along a Path

Sensor Deployment

Discover and Exposure Functions

Feasible Paths and Areas

Deployment of Additional Sensors

Conclusions