Approximation Algorithms for Constrained Relay Node Placement in Energy Harvesting Wireless Sensor Networks

The constrained relay node placement problem in a wireless sensor network seeks the deployment of a minimum number of relay nodes (RNs) in a set of candidate locations in the network to satisfy specific requirements, such as connectivity or survivability. In this paper, we study the constrained relay node placement problem in an energy-harvesting network in which the energy harvesting potential of the candidate locations are known a priori. Our aim is to place a minimum number of relay nodes, to achieve connectivity or survivability, while ensuring that the relay nodes harvest large amounts of ambient energy. We present the connectivity and survivability problems, discuss their NP-hardness, and propose polynomial time mbiO(1)-approximation algorithms with low approximation ratios to solve them. We validate the effectiveness of our algorithms through numerical results to show that the RNs placed by our algorithms harvest 50% more energy on average than those placed by the algorithms unaware of energy harvesting. We also develop a unified-mixed integer linear program (MILP)-based formulation to compute a lower bound of the optimal solution for minimum relay node placement and demonstrate that the results of our proposed algorithms were on average within 1.5 times of the optimal.