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Wireless Sensor and Actor Networks (WSANs) refer to a group of sensors and actors linked by wireless medium to probe environment and perform specific actions. Such certain actions should always be taken before a deadline when an event of interest is detected. In order to provide such services, the whole monitor area is divided into several virtual areas and nodes in the same area form a cluster. Clustering of the WSANs is often pursued to give that each actor acts as a cluster-head. The number of actors is related to the size and the deployment of WSANs cluster. In this paper, we find a method to determine the accurate number of actors which enables them to receive data and take actions in an imposed time-delay. The k-MinTE and the k-MaxTE clustering algorithm are proposed to form the minimum and maximum size of cluster, respectively. In those clustering algorithms, actors are deployed in such a way that sensors could route data to actors within k hops. Then, clusters are arranged by the regular hexagon. At last, we evaluate the placement of actors and results show that our approach is effective

Optimal Placement of Actors in WSANs Based on Imposed Delay Constraints