Pattern Mutation in Wireless Sensor Deployment

In this paper, we study the optimal deployment pattern problem in wireless sensor networks (WSNs). We propose a new set of patterns, particularly when sensors' communication range (
$r_{\rm c}$
) is relatively small compared to their sensing range (
$r_{\rm s}$
), and prove their optimality. In this study, we discover an interesting phenomenon—pattern mutation. To the best of our knowledge, this is the first time that mutation in pattern deployments has been discovered. This phenomenon, which contradicts the conjecture presented in a previous work that there exists a universal elemental pattern among optimal pattern deployment, significantly furthers our understanding of optimal patterns in WSNs.