Two-Tiered Constrained Relay Node Placement in Wireless Sensor Networks: Computational Complexity and Efficient Approximations

In wireless sensor networks, relay node placement has been proposed to improve energy efficiency. In this paper, we study two-tiered constrained relay node placement problems, where the relay nodes can be placed only at some prespecified candidate locations. To meet the connectivity requirement, we study the connected single-cover problem where each sensor node is covered by a base station or a relay node (to which 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 two base stations or relay nodes, and the relay nodes form a 2-connected network with the base stations. We study these problems under the assumption that R \ge 2r > 0, where R and r are the communication ranges of the relay nodes and the sensor nodes, respectively. We investigate the corresponding computational complexities, and propose novel polynomial time approximation algorithms for these problems. Specifically, for the connected single-cover problem, our algorithms have {\cal O}(1)-approximation ratios. For the 2-connected double-cover problem, our algorithms have {\cal O}(1)-approximation ratios for practical settings and {\cal 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 that used in an optimal solution.