| Abstract: | In this paper, we address the energy‐efficient connectivity problem of a wireless sensor network (WSN) that consists of (1) static sensor nodes that have a short communication range and limited energy level, and (2) relay nodes that have a long communication range and unlimited power supply, and that can be added or relocated arbitrarily. For such a WSN, existing studies have been focused on the design of efficient approximation algorithms to minimize the number of relay nodes. By contrast, we propose a unified backbone construction framework that can be performed in a centralized manner with two objectives: (1) to minimize the number of nodes in the backbone and (2) to maximize the lifetime of the network. To solve such a challenging problem, we formulate three subproblems: (1) partial dominating set with energy threshold (PDSET); (2) partial dominating set with largest residual energy (PDSLE); and (3) minimum relay node placement (MRNP). For these three subproblems, we develop polynomial‐time algorithms. We also prove that our algorithm for PDSLE is optimal, and our algorithm for the PDSET and MRNP problems have small approximation ratios. Numerical results show that the proposed framework can significantly improve energy efficiency and reduce backbone size. Copyright © 2012 John Wiley & Sons, Ltd. |
