Abstract
In the broadcasting of ad hoc wireless networks, energy conservation is a critical issue. Three heuristic algorithms were proposed in Wieselthier et al.(2001) for finding approximate minimum-energy broadcast routings: MST(minimum spanning tree), SPT(shortest-path tree), and BIP(broadcasting incremental power). Wan et al.(2001) characterized their performance in terms of approximation ratios. This paper points out some mistakes in the result of Wan et al.(2001), and proves that the upper bound of sum of squares of lengths of the edges in Euclidean MST in unit disk can be improved to 10.86, thus improves the approximation ratios of MST and BIP algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.-Z. Du and F.K. Hwang, “The state of art on Steiner ratio problems,” in Computing in Euclidean Geometry, D.-Z. Du and F.K. Hwang (eds.), World Scientific, 1992.
F.P. Preparata and M.I. Shamos, Computational Geometry: an Introduction, Springer-Verlag, 1985.
T.S. Rappaport, Wireless Communications Principles and Practices, Prentice Hall, 1996.
P.J. Wan, G. Calinescu, X.Y. Li, and O. Frieder, “Minimum-energy broadcast routing in static ad hoc wireless networks,” in IEEE INFOCOM ‘2001, 2001.
J.E. Wieselthier, G.D. Nguyen, and A. Ephremides, “On the construction of energy-efficient broadcast and multicast trees in wireless networks,” in IEEE INFOCOM ‘2000, 2000.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by Natural Science Foundation of China (60223004, 603210022)
Rights and permissions
About this article
Cite this article
Cai, H., Zhao, Y. On Approximation Ratios of Minimum-Energy Multicast Routing in Wireless Networks. J Comb Optim 9, 243–262 (2005). https://doi.org/10.1007/s10878-005-1409-4
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10878-005-1409-4