K-coverage in regular deterministic sensor deployments

An area is k-covered if every point of the area is covered by at least k sensors. K-coverage is necessary for many applications, such as intrusion detection, data gathering, and object tracking. It is also desirable in situations where a stronger environmental monitoring capability is desired, such as military applications. In this paper, we study the problem of k-coverage in deterministic homogeneous deployments of sensors. We examine the three regular sensor deployments - triangular, square and hexagonal deployments - for k-coverage of the deployment area, for k ≥ 1. We compare the three regular deployments in terms of sensor density. For each deployment, we compute an upper bound and a lower bound on the optimal distance of sensors from each other that ensure k-coverage of the area. We present the results for each k from 1 to 20 and show that the required number of sensors to k-cover the area using uniform random deployment is approximately 3-10 times higher than regular deployments

On the Displacement for Covering a d−d-dimensional Cube with Randomly Placed Sensors

Consider $n$ sensors placed randomly and independently with the uniform distribution in a $d-$dimensional unit cube ($d\ge 2$). The sensors have identical sensing range equal to $r$, for some $r >0$. We are interested in moving the sensors from their initial positions to new positions so as to ensure that the $d-$dimensional unit cube is completely covered, i.e., every point in the $d-$dimensional cube is within the range of a sensor. If the $i$-th sensor is displaced a distance $d_i$, what is a displacement of minimum cost? As cost measure for the displacement of the team of sensors we consider the $a$-total movement defined as the sum $M_a:= \sum_{i=1}^n d_i^a$, for some constant $a>0$. We assume that $r$ and $n$ are chosen so as to allow full coverage of the $d-$dimensional unit cube and $a > 0$. The main contribution of the paper is to show the existence of a tradeoff between the $d-$dimensional cube, sensing radius and $a$-total movement. The main results can be summarized as follows for the case of the $d-$dimensional cube. If the $d-$dimensional cube sensing radius is $\frac{1}{2n^{1/d}}$ and $n=m^d$, for some $m\in N$, then we present an algorithm that uses $O\left(n^{1-\frac{a}{2d}}\right)$ total expected movement (see Algorithm 2 and Theorem 5). If the $d-$dimensional cube sensing radius is greater than $\frac{3^{3/d}}{(3^{1/d}-1)(3^{1/d}-1)}\frac{1}{2n^{1/d}}$ and $n$ is a natural number then the total expected movement is $O\left(n^{1-\frac{a}{2d}}\left(\frac{\ln n}{n}\right)^{\frac{a}{2d}}\right)$ (see Algorithm 3 and Theorem 7). In addition, we simulate Algorithm 2 and discuss the results of our simulations

Simulasi Coverage Wireless Sensor Network dengan Sum of Weighted Cost Function Genetic Algorithm

Masalah coverage pada wireless sensor network (WSN) adalah untuk meletakan sensor pada service area yang dapat mencakup seluruh service area. Masalah coverage dalam WSN sangat penting karena merepresentasikan QoS (Quality of Service) dari WSN tersebut. Pada paper ini akan disajikan sebuah simulasi untuk merancang sebuah system dengan coverage area yang optimal dengan sebuah algorithma genetika yang dikombinasikan dengan sum of weighted cost functions untuk penentuan komposisi berbagai macam letak dan jenis sensor yang dapat mengkover area seluas-luasnya dan dengan biaya seminimal mungkin. Dengan sum of weighted cost functions, perbandingan kedua fungsi dapat diatur, sehingga didapatkan optimisasi pada kedua fungsi tersebut. Fungsi-fungsi dalam hal ini adalah fungsi cost function yang merepresentasikan biaya total WSN dan fitness function yang merepresentasikan coverage sensor nodes

Analisa Kinerja dan Simulasi Coverage Wireless Sensor Network dengan Sum of Weighted Cost Function Genetic Algorithm

Masalah coverage pada wireless sensor network (WSN) adalah untuk meletakan sensor pada service area yang dapat mencakup seluruh service area. Masalah coverage dalam WSN sangat penting karena merepresentasikan QoS (Quality of Service) dari WSN tersebut. Pada paper ini akan disajikan sebuah simulasi untuk merancang sebuah system dengan coverage area yang optimal dengan sebuah algorithma genetika yang dikombinasikan dengan sum of weighted cost functions untuk penentuan komposisi berbagai macam letak dan jenis sensor yang dapat mengkover area seluas-luasnya dan dengan biaya seminimal mungkin. Dengan sum of weighted cost functions, perbandingan kedua fungsi dapat diatur, sehingga didapatkan optimisasi pada kedua fungsi tersebut. Fungsi-fungsi dalam hal ini adalah fungsi cost function yang merepresentasikan biaya total WSN dan fitness function yang merepresentasikan coverage sensor nodes

On perimeter coverage in wireless sensor networks

Many sensor network applications require the tracking and the surveillance of target objects. However, in current research, many studies have assumed that a target object can be sufficiently monitored by a single sensor. This assumption is invalid in some situations, especially, when the target object is so large that a single sensor can only monitor a certain portion of it. In this case, several sensors are required to ensure a 360 coverage of the target. To minimize the amount of energy required to cover the target, the minimum set of sensors should be identified. Centralized algorithms are not suitable for sensor applications. In this paper, we describe our novel distributed algorithm for finding the minimum cover. Our algorithm requires fewer messages than earlier mechanisms and we provide a formal proof of correctness and time of convergence. We further demonstrate our performance improvement through extensive simulations. © 2006 IEEE.published_or_final_versio