A wireless sensor network (WSN) is a network of distributed nodes, each equipped with sensors, computational elements, and transceivers. These networks are able to sense a desired phenomenon over a large geographic region and communicate this information back to the user or to a sink. While the use of these networks has been demonstrated, their full capabilities have not been realized, primarily due to the lack of efficient algorithms for self organization and fault tolerant operation. A fundamental issue in the deployment of a large scale WSN is the ability of the network to cover the region of interest. While it is important to know if the region is covered by the deployed sensor nodes, it is of even greater importance to determine the minimum number of these deployed sensors that will still guarantee coverage of the region. This issue takes on added importance as the sensor nodes have limited battery power. In this book, the coverage problem in a three dimensional space is rigorously analyzed and the minimum number of sensor nodes and their placement for complete coverage is determined.

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