Advertisement

An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks

  • Christoph Ambühl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)

Abstract

Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33-approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.

Keywords

Wireless Network Convex Hull Equilateral Triangle Broadcast Tree Half Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bar-Yehuda, R., Goldreich, O., Itai, A.: On the Time Complexity of Broadcast Operations in Multi-Hop Radio Networks: An Exponential Gap Between Determinism and Randomization. Journal of Computer and Systems Science 45, 104–126 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bar-Yehuda, R., Israeli, A., Itai, A.: Multiple Communication in Multi-Hop Radio Networks. SIAM Journal on Computing 22, 875–887 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    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. Technical Report 010, University of Rome “Tor Vergata”, Math Department (2001)Google Scholar
  4. 4.
    Clementi, A.E.F., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs. In: Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 121–131 (2001)Google Scholar
  5. 5.
    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: Proceedings of the 3rd Workshop on Approximation and Randomization Algorithms in Communication Networks (ARACNE), pp. 23–38 (2002)Google Scholar
  6. 6.
    Clementi, A.E.F., Huiban, G., Penna, P., Rossi, G., Verhoeven, Y.C.: On the Approximation Ratio of the MST-based Heuristic for the Energy-Efficient Broadcast Problem in Static Ad-Hoc Wireless Networks. In: 3rd Workshop on Wireles, Mobile and Ad-Hoc Networks (WMAN) in the Proceedigs of the 17th International Parallel and Distributed Precessing Symposium, IPDPS (2003)Google Scholar
  7. 7.
    Ephremides, A., Nguyen, G.D., Wieselthier, J.E.: On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks. In: Proceedings of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pp. 585–594 (2000)Google Scholar
  8. 8.
    Flammini, M., Klasing, R., Navarra, A., Perennes, S.: Improved approximation results for the minimum energy broadcasting problem. In: Proceedings of the 2004 joint workshop on Foundations of mobile computing (2004)Google Scholar
  9. 9.
    Gilbert, E.N., Pollak, H.O.: Steiner minimal trees. SIAM Journal on Applied Mathematics 16(1), 1–29 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Guha, S., Khuller, S.: Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets. Information and Computation 150, 57–74 (1999)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Haas, Z., Tabrizi, S.: On Some Challenges and Design Choices in Ad-Hoc Communications. In: Proceedings of the IEEE Military Communication Conference, MILCOM (1998)Google Scholar
  12. 12.
    Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. Theoretical Computer Science 243, 289–305 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Klasing, R., Navarra, A., Papadopoulos, A., Perennes, S.: Adaptive broadcast consumption (abc), a new heuristic and new bounds for the minimum energy broadcast routing problem, pp. 866–877 (2004)Google Scholar
  14. 14.
    Lauer, G.S.: Packet radio routing. In: Streenstrup, M. (ed.) Routing in communication networks, ch. 11, pp. 351–396. Prentice-Hall, Englewood Cliffs (1995)Google Scholar
  15. 15.
    Navarra, A., Flammini, M., Perennes, S.: The “real” approximation factor of the mst heuristic for the minimum energy broadcasting, pp. 22–31 (2005)Google Scholar
  16. 16.
    Montemanni, R., Gambardella, L.M.: Exact algorithms for the minimum power symmetric connectivity problem in wireless networks. Computers and Operations Research (to appear)Google Scholar
  17. 17.
    Montemanni, R., Gambardella, L.M., Das, A.K.: Mathematical models and exact algorithms for the min-power symmetric connectivity problem: an overview. In: Wu, J. (ed.) Handbook on Theoretical and Algorithmic Aspects of Sensor, Ad Hoc Wireless, and Peer-to-Peer Networks. CRC Press, Boca Raton (to appear)Google Scholar
  18. 18.
    Navarra, A.: Tighter bounds for the minimum energy broadcasting problem, pp. 313–322 (2005)Google Scholar
  19. 19.
    Pahlavan, K., Levesque, A.: Wireless Information Networks. Wiley Interscience, Hoboken (1995)Google Scholar
  20. 20.
    Steele, J.M.: Cost of sequential connection for points in space. Operations Research Letters 8(3), 137–142 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Wan, P.J., Cǎlinescu, G., Li, X.Y., Frieder, O.: Minimum-Energy Broadcast Routing in Static Ad Hoc Wireless Networks. In: Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pp. 1162–1171 (2001)Google Scholar
  22. 22.
    Weisstein, E.W.: MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christoph Ambühl
    • 1
  1. 1.Department of Computer ScienceThe University of Liverpool 

Personalised recommendations