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EBSCO Publishing : eBook Collection (EBSCOhost) - printed on 2/16/2016 3:46 AM via CGC-GROUP OF COLLEGES (GHARUAN) AN: 340572 ; Beyah, Raheem, Corbett, Cherita, McNair, Janise.; Security in Ad Hoc and Sensor Networks Account: ns224671
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Key Pre-Distribution for Sensor Networks Using Group Deployment Knowledge 71 very likely that they are affected in a similar way by the same set of factors. Therefore, the final locations of the nodes in the same group will be close to each other with a high probability after deployment. Based on the above discussion, we present a practical deployment model in this subsection. In this model, the sensor nodes are only required to be deployed in groups. The deployment knowledge used to improve key pre- distribution is the observation that the sensor nodes in the same group are usually close to each other after deployment. This model in fact is more practical and requires less efforts in the deployment of sensor nodes than the models where the sensor nodes need to be placed close to their expected locations. For example, a group of sensor nodes may only need to be dropped from the airplane at the same time. For the sake of presentation, we call a group of sensor nodes that need to be deployed together as a deployment group . We assume that the sensor nodes are static once they are deployed. We define the resident point of a sensor node as the point location where this sensor node finally resides. The sensors’ resident points are generally different from each other even for the sensor nodes in the same group. However, in our later evaluation, we assume the resident points of the sensor nodes in the same group follow the same probability distribution function for simplicity, though the proposed method will still work under different distribution functions. The detailed description of the proposed deployment model is given below. The sensor nodes to be deployed are divided into n deployment groups { G i } i =1 ,...,n . We assume that these groups are evenly and independently deployed in a target field. The sensor nodes in the same deployment group G i are deployed from the same place at the same time with the deployment index i . During the deployment of any group G i , the resident point of any sensor node in this group follows a probability distribution function (pdf) f i ( x, y ), which we call the deployment distribution of group G i . An example of the pdf f i ( x, y ) is a two-dimensional Gaussian distribution. Figure 1 illustrates a two-dimensional Gaussian distribution with center (150 , 150). The actual deployment distribution is affected by many factors. For simplicity, we model the deployment distribution as a Gaussian distribution (also called Normal distribution) since it is widely studied and proved to be useful in practice. Although we only employ the Gaussian distribution in our evaluation, our methodology can be applied to other distributions as well.
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