Wireless sensor networks require energy-efficient data transmission because the sensor nodes have limited power. A cluster-based routing method is more energy-efficient than a flat routing method as it can only send specific data for user requirements and aggregate similar data by dividing a network into a local cluster. However, previous clustering algorithms have some problems in that the transmission radius of sensor nodes is not realistic and multi-hop based communication is not used both inside and outside local clusters. As energy consumption based on clustering is dependent on the number of clusters, we need to know how many clusters are best. Thus, we propose an optimal number of cluster-heads based on multi-hop routing in wireless sensor networks. We observe that a local cluster made by a cluster-head influences the energy consumption of sensor nodes. We determined an equation for the number of packets to send and relay, and calculated the energy consumption of sensor networks using it. Through the process of calculating the energy consumption, we can obtain the optimal number of cluster-heads in wireless sensor networks.
Keywords: clustering method; multi-hop routing; optimal cluster-heads; sensor networks.