The “Real” Approximation Factor of the MST Heuristic for the Minimum Energy Broadcasting

  • Michele Flammini
  • Alfredo Navarra
  • Stephane Perennes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


The paper deals with one of the most studied problems during the last years in the field of wireless communications in Ad-Hoc networks. The problem consists in reducing the total energy consumption of wireless radio stations randomly spread on a given area of interest to perform the basic pattern of communication given by the Broadcast. Recently an almost tight 6.33-approximation of the Minimum Spanning Tree heuristic has been proved [8]. While such a bound is theoretically close to optimum compared to the known lower bound of 6 [10], there is an evident gap with practical experimental results. By extensive experiments, proposing a new technique to generate input instances and supported by theoretical results, we show how the approximation ratio can be actually considered close to 4 for a “real world” set of instances, that is, instances with a number of nodes more representative of practical purposes.


High Degree Node Range Assignment Minimum Span Tree Cost Directed Span Tree Complete Weighted Graph 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Athanassopoulos, S., Caragiannis, I., Kaklamanis, C., Kanellopoulos, P.: Experimental Comparison of Algorithms for Energy-Efficient Multicasting in Ad Hoc Networks. In: Nikolaidis, I., Barbeau, M., Kranakis, E. (eds.) ADHOC-NOW 2004. LNCS, vol. 3158, pp. 183–196. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Clementi, A., 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 radio networks. In: Proceedings of the 3rd IEEE IPDPS Workshop on Wireless, Mobile and Ad Hoc Networks, WMAN (2003)Google Scholar
  3. 3.
    Clementi, A.E.F., Crescenzi, P., Penna, P., Rossi, G., Vocca, P.: On the complexity of computing minimum energy consumption broadcast subgraph. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 121–131. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Flammini, M., Klasing, R., Navarra, A., Perennes, S.: Improved approximation results for the Minimum Energy Broadcasting Problem. In: Proceedings of ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), pp. 85–91 (2004)Google Scholar
  5. 5.
    Frieze, A.M., McDiarmid, C.J.H.: On Random Minimum Length Spanning Trees. Combinatorica 9, 363–374 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    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. 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)CrossRefGoogle Scholar
  7. 7.
    Martínez, F.J.O., Stojmenovic, I., Nocetti, F.G., Gonzalez, J.S.: Finding Minimum Transmission Radii for Preserving Connectivity and Constructing Minimal Spanning Trees in Ad Hoc and Sensor Networks. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 369–382. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Navarra, A.: Tighter bounds for the Minimum Energy Broadcasting problem. In: Proceedings of the 3rd International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt (2005) (to appear)Google Scholar
  9. 9.
    Penna, P., Ventre, C.: Energy-efficient broadcasting in ad-hoc networks: combining msts with shortest-path trees. In: Proceedings of the 1st ACM International Workshop on Performance Evaluation of Wireless, Ad Hoc, Sensor and Ubiquitous Networks (PE-WASUN), pp. 61–68. ACM Press, New York (2004)CrossRefGoogle Scholar
  10. 10.
    Wan, P.J., Calinescu, G., Li, X., Frieder, O.: Minimum energy broadcasting in static ad hoc wireless networks. Wireless Networks 8(6), 607–617 (2002): Extended abstract appeared. In: Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM) (2001)Google Scholar
  11. 11.
    Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: 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. IEEE Computer Society, Los Alamitos (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michele Flammini
    • 1
  • Alfredo Navarra
    • 1
  • Stephane Perennes
    • 2
  1. 1.Computer Science DepartmentUniversity of L’AquilaL’AquilaItaly
  2. 2.MASCOTTE projectI3S-CNRS/INRIA/University of NiceSophia AntipolisFrance

Personalised recommendations