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Journal of Sensors
Volume 2015 (2015), Article ID 565983, 12 pages
Research Article

Linear Time Approximation Algorithms for the Relay Node Placement Problem in Wireless Sensor Networks with Hexagon Tessellation

1Department of Information Engineering, I-Shou University, Kaohsiung 84001, Taiwan
2Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan

Received 26 June 2014; Revised 9 September 2014; Accepted 20 March 2015

Academic Editor: Chenzhong Li

Copyright © 2015 Chi-Chang Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The relay node placement problem in wireless sensor network (WSN) aims at deploying the minimum number of relay nodes over the network so that each sensor can communicate with at least one relay node. When the deployed relay nodes are homogeneous and their communication ranges are circular, one way to solve the WSN relay node placement problem is to solve the minimum geometric disk cover (MGDC) problem first and place the relay nodes at the centers of the covering disks and then, if necessary, deploy additional relay nodes to meet the connection requirement of relay nodes. It is known that the MGDC problem is NP-complete. A novel linear time approximation algorithm for the MGDC problem is proposed, which identifies covering disks using the regular hexagon tessellation of the plane with bounded area. The approximation ratio of the proposed algorithm is (), where . Experimental results show that the worst case is rare, and on average the proposed algorithm uses less than 1.7 times the optimal disks of the MGDC problem. In cases where quick deployment is necessary, this study provides a fast 7-approximation algorithm which uses on average less than twice the optimal number of relay nodes in the simulation.