Deploying Four-Connectivity and Full-Coverage Wireless Sensor Networks

Abstract

We study the issue of optimal deployment to achieve four connectivity and full coverage for wireless sensor networks (WSNs) under different ratios of sensors' communication range (denoted by r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) to their sensing range (denoted by r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ). We propose a "Diamond" pattern, which can be viewed as a series of different evolving patterns. When r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> /r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ges radic3, the Diamond pattern coincides with the well-known triangle lattice pattern; when r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> /r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ges radic2, it degenerates to a "Square" pattern. We prove the Diamond pattern to be asymptotically optimal when r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> /r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ges radic2- Our work is the first to propose an asymptotically optimal deployment pattern to achieve four connectivity and full coverage for WSNs. We hope our work will provide some insights on how optimal patterns evolve and how to search for them.