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Clustering sensor nodes is an efficient technique to improve scalability and life time of a wireless sensor network (WSN). However, in a cluster based WSN, the leaders (cluster heads) consume more energy due to some extra load for various activities such as data collection, data aggregation, and communication of the aggregated data to the base station. Therefore, balancing the load of the cluster heads is a crucial issue for the long run operation of the WSNs. In this paper, we first present a load balanced clustering scheme for wireless sensor networks. We show that the algorithm runs in O(nlogn) time for n sensor nodes. We prove that the algorithm is optimal for the case in which the sensor nodes have equal load. We also show that it is a polynomial time 2-approximation algorithm for the general case, i.e., when the sensor nodes have variable load. We finally improve this algorithm and propose a 1.5 …