Optimal Placement of Relay Nodes in Two-Tiered, Fault Tolerant Sensor Networks

Nodes in sensor networks are often prone to failure, particularly when deployed in hostile territories, where chances of damage/destruction are significantly higher. There is also the possibility for the loss of connectivity between nodes due to the inherent limitations of the wireless communication medium. Therefore, a sensor network should be designed in such a way that the network is able to continue to operate, even if some of the nodes/links in the network fail. The scalability and the lifetime of sensor networks are affected by the limited transmission range and the battery power of sensor nodes. Recently, relay nodes have been proposed for balanced data gathering, reduction of transmission range, connectivity and fault tolerance. In hierarchical sensor networks using relay nodes, sensor nodes are arranged in clusters and higher-powered relay nodes can be used as cluster heads. Finding the minimum number of such relay nodes, along with their locations, so that each sensor node can communicate with at least k_s (k_s = 1,2...) relay nodes and the relay node network is k_r-connected (k_r = 1,2...), is known to be a difficult problem. Some recent works in this area have proposed heuristic solutions for the the special cases of k_s = 1 or 2 and k_r = 1 or 2. In this paper, we have presented a generalized integer linear program (ILP) formulation capable of generating exact solutions for arbitrary values of k_s and k_r.