In Wireless Sensor Networks (WSNs) energy is a scarce resource which must be utilized efficiently in order to enhance the network lifetime. Two-Tiered Wireless Sensor Network (TT-WSN) architecture is proposed to improve the lifetime longevity of the network. In TT-WSN the lower tier consists of sensor nodes (SN), which are mainly responsible for sensing the environment and forwarding the data to its one hop neighbor relay node (RN). While the upper tier is constituent of more power affluent relay nodes (RNs), which deliver the data to the base station through potentially multiple connected relay nodes in a multi-hop fashion. As relay nodes are more expensive, it is therefore desirable to deploy a minimum number of such nodes so that every sensor node has at least one relay node as its one-hop neighbor and all the relay nodes form a connected network. Unfortunately the problem of finding such a minimum set of relay nodes is NP-Hard. Thus an approximation based algorithm is required to solve the problem in polynomial time. Existing solutions are either very complex or less efficient. In this paper we present a fast approximation algorithm to solve the problem in polynomial time. The performance of the algorithm is compared with the existing algorithms through simulations. The extensive simulation results show that our algorithm outperforms the existing algorithms in terms of number of relay nodes deployed.
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