Two-tiered constrained relay node placement in wireless sensor networks: Efficient approximations

In a wireless sensor network, short range multihop transmissions are preferred to prolong the network lifetime due to super-linear nature of energy consumption with communication distance. It has been proposed to deploy some relay nodes such that the sensors can transmit the sensed data to a nearby relay node, which in turn delivers the data to the base stations. In general, the relay node placement problems aim to meet certain connectivity and/or survivability requirements of the network by deploying a minimum number of relay nodes. In this paper, we study two-tiered constrained relay node placement problems, where the relay nodes can only be placed at some pre-specified candidate locations. To meet the connectivity requirement, we study the connected single-cover problem where each sensor node is covered by a relay node (to whom the sensor node can transmit data), and the relay nodes form a connected network with the base stations. To meet the survivability requirement, we study the 2-connected double-cover problem where each sensor node is covered by at least two relay nodes, and the relay nodes form a 2-connected network with the base stations. We focus on the computational complexities of the problems, and propose novel polynomial time approximation algorithms for these problems. For the connected single-cover problem, our algorithms have O(1) approximation ratios. For the 2-connected double-cover problem, our algorithms have O(1) approximation ratios for practical settings and O(ln n) approximation ratios for arbitrary settings. Experimental results show that the number of relay nodes used by our algorithms is no more than twice of the number of relay nodes used in an optimal solution.