Minimal and maximal exposure path algorithms for wireless embedded sensor networks

Abstract

Sensor networks not only have the potential to change the way we use, interact with, and view computers, but also the way we use, interact with, and view the world around us. In order to maximize the effectiveness of sensor networks, one has to identify, examine, understand, and provide solutions for the fundamental problems related to wireless embedded sensor networks. We believe that one of such problems is to determine how well the sensor network monitors the instrumented area. These problems are usually classified as coverage problems. There already exist several methods that have been proposed to evaluate a sensor network's coverage.We start from one of such method and provide a new approach to complement it. The method of using the minimal exposure path to quantify coverage has been optimally solved using a numerical approximation approach. The minimal exposure path can be thought of as the worst-case coverage of a sensor network. Our first goal is to develop an efficient localized algorithm that enables a sensor network to determine its minimal exposure path. The theoretical highlight of this paper is the closed-form solution for minimal exposure in the presence of a single sensor. This solution is the basis for the new and significantly faster localized approximation algorithm that reduces the theoretical complexity of the previous algorithm. On the other hand, we introduce a new coverage problem -the maximal exposure path -which is in a sense the best-case coverage path for a sensor network. We prove that the maximal exposure path problem is NP-hard, and thus, we provide heuristics to generate approximate solutions.In addition, we demonstrate the effectiveness of our algorithms through several simulations. In the case of the minimal singlesource minimal exposure path, we use variational calculus to determine exact solutions. For the case of maximal exposure, we use networks with varying numbers of sensors and exposure models.

Percolation-theory based density derivations of wireless sensor network nodes for preventing exposure paths

“…Paper [5] was the first to identify the importance of computational geometry and Voronoi Diagrams in sensor network coverage. Paper [9] considers how does one traverse through the sensor field from one point to another such that the sensors have the least or most coverage of the traveled path. Paper [6], [7] and [8] use the least-covered path to measure the ability to move in the sensor field without being discovered.…”

Dynamic heuristic anti-monitoring path searching algorithm in sensory field

“…Current works on anti-monitoring problem of mobile object mainly adopt the following methods, first partition the whole field into discrete Grids [2][3] [6] or Voronoi [4][5] [7] [8] beehives, then on the basis of different definition of the exposure to them, path searching algorithm can be implemented to generate a optimum path for the mobile object to get across through the sensory field.…”

“…In reference [8], next positions are determined from partitioned Voronoi beehives, and exposure degree is defined as the signal strength the sensor network received from mobile object. From the perspective of t he partition method, Voronoi beehives ensure that all the points in a beehive are close or closer to the centre than all the points out side of the beehive to the centre, but as a matter of fact, in case like dense sensor distribution, the VORONOI beehive partition can not generate safe selection; in a simple square grid, the mobile object only can move along vertical or horizontal direction, which obviously make the path more complex for the mobile object.…”

“…From the perspective of t he partition method, Voronoi beehives ensure that all the points in a beehive are close or closer to the centre than all the points out side of the beehive to the centre, but as a matter of fact, in case like dense sensor distribution, the VORONOI beehive partition can not generate safe selection; in a simple square grid, the mobile object only can move along vertical or horizontal direction, which obviously make the path more complex for the mobile object. Reference [2][4] [8] are centralized algorithm, which means that the mobile object has to know all the location information of the sensors, it is not practical in real application. Reference [5] is distributed, but Voronoi partition is limited in performance.…”

Navigation protocols in sensor networks

“…In our article, we consider a specific application, navigation problem. Meguerdichian et al [2001] and Veltri et al [2003] considered the minimal and maximal exposure path problem in a network. We consider a seemingly similar problem.…”