Abstract
We consider the problem of minimizing the total energy assigned to nodes of wireless network so that broadcasting from the source node to all other nodes is possible. This problem has been extensively studied especially under the assumption that the nodes correspond to points in the Euclidean two- or three-dimensional space and the broadcast range of a node is proportional to at most the α root of the energy assigned to the node where α is not less than the dimension d of the space. In this paper, we study the case α≤d, providing several tight upper and lower bounds on approximation factors of known heuristics for minimum energy broadcasting in the d-dimensional Euclidean space.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ambühl, C.: An optimal bound for the MST algorithm to compute energy efficient broadcast trees in wireless networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1139–1150. Springer, Heidelberg (2005)
Bronnimann, H., Goodrich, M.T.: Almost Optimal Set Covers in Finite VC-Dimension. In: Proc. 10th Annual ACM Symposium on Computational Geometry (SCG 1994), pp. 293–302. ACM Press, New York (1994)
Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network Lifetime and Power Assignment in ad hoc Wireless Networks. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 114–126. Springer, Heidelberg (2003)
Caragiannis, I., Kaklamanis, C.: New results for energy-efficient broadcasting in wireless networks. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 332–343. Springer, Heidelberg (2002)
Clarksson, K.L., Varadarajan, K.: Improved Approximation Algorithms for Geometric Set Cover. In: Proc. 21st Annual ACM Symposium on Computational Geometry (SCG 2005), pp. 135–141. ACM Press, New York (2005)
Clementi, A.E.F., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: On the complexity of computing minimum energy consumption broadcast subgraphs. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 121–131. Springer, Heidelberg (2001)
Clementi, A.E.F., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: A Worst-case Analysis of an MST-based Heuristic to Construct Energy-Efficient Broadcast Trees in Wireless Networks. Manuscript
Clementi, A.E.F., Huiban, G., Penna, P., Rossi, G., Verhoeven, Y.C.: Some Recent Theoretical Advances and Open Questions on Energy Consumption in Ad-Hoc Wireless Networks. In: Proc. 3rd Workshop on Approximation and Randomization Algorithms in Communication Networks (ARACNE 2002), pp. 23–38 (2002)
Flammini, M., Klasing, R., Navarra, A., Pérennes, S.: Improved approximation results for the minimum energy broadcasting problem. In: Proc. of the 2004 joint workshop on Foundations of mobile computing (DIALM-POMC 2004), pp. 85–91. ACM Press, New York (2004)
Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)
Goodman, J.E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry. Chapman & Hall/CRC, Boca Raton (2004)
Haas, Z., Tabrizi, S.: On Some Challenges and Design Choices in Ad-Hoc Communications. In: Proc. of the IEEE Military Communication Conference (MILCOM 1998), pp. 187–192 (1998)
Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. Theoretical Computer Science 243, 289–305 (2000)
Klasing, R., Navarra, A., Papadopoulos, A., Pérénnes, S.: Adaptive broadcast consumption (ABC), a new heuristic and new bounds for the minimum energy broadcast routing problem. In: Mitrou, N.M., Kontovasilis, K., Rouskas, G.N., Iliadis, I., Merakos, L. (eds.) NETWORKING 2004. LNCS, vol. 3042, pp. 866–877. Springer, Heidelberg (2004)
Lauer, G.S.: Packet radio routing, ch.11. In: Streenstrup, M. (ed.) Routing in communication networks, pp. 351–396. Prentice-Hall, Englewood Cliffs (1995)
Li, G., Fan, P., Cai, K.: On the geometrical characteristics of three dimensional wireless ad-hoc networks and its applications. EURASIP Journal on Wireless Communications & Networking (to appear)
Liang, W.: Constructing minimum-energy broadcast trees in wireless ad hoc networks. In: Proc. 3rd ACM International Symposium on Mobile Ad Hoc Networking & Computing (MobiHoc 2002), pp. 112–122. ACM Press, New York (2002)
Navarra, A.: Tighter bounds for the minimum energy broadcasting problem. In: Proc. 3rd International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt 2005), pp. 313–322. IEEE Computer Society, Los Alamitos (2005)
Wan, P.J., Calinescu, G., Li, X.Y., Frieder, O.: Minimum-energy broadcast routing in static ad hoc wireless networks. In: Proc. 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), pp. 1162–1171 (2001)
Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: On the construction of energy-efficient broadcast and multicast trees in wireless networks. In: Proc. 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2000), pp. 585–594 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lingas, A., Persson, M., Wahlen, M. (2006). Minimum-Energy Broadcasting in Wireless Networks in the d-Dimensional Euclidean Space (The α≤d Case). In: Erlebach, T. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2006. Lecture Notes in Computer Science, vol 4235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922377_10
Download citation
DOI: https://doi.org/10.1007/11922377_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48822-4
Online ISBN: 978-3-540-48824-8
eBook Packages: Computer ScienceComputer Science (R0)