Abstract
In the design of wireless networks, techniques for improving energy efficiency and extending network lifetime have great importance, particularly for defense and civil/rescue applications where resupplying transmitters with new batteries is not feasible. In this paper we study a method for improving the lifetime of wireless networks by minimizing the length of the longest edge in the interconnecting tree by deploying additional relay nodes at specific locations. This optimization problem, known as the Bottleneck Steiner Tree Problem (BSTP), asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. We present a ratio- \(\sqrt{3}+\epsilon\) polynomial time approximation algorithm for BSTP, where \(\epsilon\) is an arbitrary positive number.
Similar content being viewed by others
References
Chen D., Du D.-Z., Hu X., Lin G., Wang L., Xue G. (2000) Approximations for Steiner trees with minimum number of Steiner points. J. Global Optim. 18, 17–33
Chang, J.-H., Tassiulas, L. Fast approximate algorithms for maximum lifetime routing in wireless ad-hoc networks. Lecture Notes in Computer Science, 1815 pp. 702–713 Springer (2000)
Chang, J.-H., Tassiulas, L. Energy conserving routing in wireless ad-hoc networks. Proceedings of the 19th Annual IEEE Infocom Conference (2000)
Chiang C., Sarrafzadeh M., Wong C.K. (1990) A powerful global router: based on Steiner min-max tree. IEEE Trans. Comput.-Aided Desig 19, 1318–1325
Lin G., Xue G. (1999) Steiner tree problem with minimum number of Steiner points and bounded edge-length. Inform. Process. Lett. 69:53–57
Li Q., Aslam J., Rus D. Online power-aware routing in wireless ad-hoc networks. Proceedings of ACM SIGMOBILE, pp. 97–107 (2001)
Prömel H.J., Steger A. (2000) A new approximation algorithm for the steiner tree problem with performance ratio 5/3. J. Algor. 36, 89–101
Sarrafzadeh M., Wong C.K. (1992) Bottleneck Steiner trees in the plane. IEEE Trans. Comput. 41:370–374
Slijepcevic, S., Potkonjak, M. Power efficient organization of wireless sensor networks. IEEE International Conference on Communications (ICC), June 2001, Helsinki, Finland
Wang L., Du D.-Z. (2002) Approximations for a Bottleneck Steiner Tree Problem. Algorithmica 32:554–561
Wang L., Li Z. (2002) An approximation algorithm for a Bottleneck Steiner Tree Problem in the Euclidean plane. Inform. Process. Lett. 81:151–156
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cardei, I., Cardei, M., Wang, L. et al. Optimal Relay Location for Resource-limited Energy-efficient Wireless Communication. J Glob Optim 36, 391–399 (2006). https://doi.org/10.1007/s10898-006-9017-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9017-0