Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Degree-Bounded Planar Spanner with Low Weight

2005; Song, Li, Wang
  • Wen-Zhan Song
  • Xiang-Yang Li
  • Weizhao Wang
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_103

Keywords and Synonyms

Unified energy-efficient unicast and broadcast topology control                

Problem Definition

An important requirement of wireless ad hoc networks is that they should be self‐organizing, and transmission ranges and data paths may need to be dynamically restructured with changing topology. Energy conservation and network performance are probably the most critical issues in wireless ad hoc networks, because wireless devices are usually powered by batteries only and have limited computing capability and memory. Hence, in such a dynamic and resource‐limited environment, each wireless node needs to locally select communication neighbors and adjust its transmission power accordingly, such that all nodes together self-form a topology that is energy efficient for both unicast and broadcast communications.

To support energy‐efficient unicast, the topology is preferred to have the following features in the literature:

  1. 1.

    Power Spanner: [1,9,13,16,17] Formally...

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Bose, P., Gudmundsson, J., Smid, M.: Constructing plane spanners of bounded degree and low weight. In: Proceedings of European Symposium of Algorithms, University of Rome, 17–21 September 2002Google Scholar
  2. 2.
    Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. ACM/Kluwer Wireless Networks 7(6), 609–616 (2001). 3rd int. Workshop on Discrete Algorithms and methods for mobile computing and communications, 48–55 (1999)zbMATHCrossRefGoogle Scholar
  3. 3.
    Burkhart, M., von Rickenbach, P., Wattenhofer, R., Zollinger, A.: Does topology control reduce interference. In: ACM Int. Symposium on Mobile Ad-Hoc Networking and Computing (MobiHoc), Tokyo, 24–26 May 2004Google Scholar
  4. 4.
    Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic variation analysis. Syst. Zool. 18, 259–278 (1969)CrossRefGoogle Scholar
  5. 5.
    Karp, B., Kung, H.T.: Gpsr: Greedy perimeter stateless routing for wireless networks. In: Proc. of the ACM/IEEE International Conference on Mobile Computing and Networking (MobiCom), Boston, 6–11 August 2000Google Scholar
  6. 6.
    Kleinrock, L., Silvester, J.: Optimum transmission radii for packet radio networks or why six is a magic number. In: Proceedings of the IEEE National Telecommunications Conference, pp. 431–435, Birmingham, 4–6 December 1978Google Scholar
  7. 7.
    Kuhn, F., Wattenhofer, R., Zollinger, A.: Asymptotically optimal geometric mobile ad-hoc routing. In: International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIALM), Atlanta, 28 September 2002Google Scholar
  8. 8.
    Kuhn, F., Wattenhofer, R., Zollinger, A.: Worst-case optimal and average-case efficient geometric ad-hoc routing. In: ACM Int. Symposium on Mobile Ad-Hoc Networking and Computing (MobiHoc) Anapolis, 1–3 June 2003Google Scholar
  9. 9.
    Li, L., Halpern, J.Y., Bahl, P., Wang, Y.-M., Wattenhofer, R.: Analysis of a cone-based distributed topology control algorithms for wireless multi-hop networks. In: PODC: ACM Symposium on Principle of Distributed Computing, Newport, 26–29 August 2001Google Scholar
  10. 10.
    Li, X.-Y.: Approximate MST for UDG locally. In: COCOON, Big Sky, 25–28 July 2003Google Scholar
  11. 11.
    Li, X.-Y., Wan, P.-J., Wang, Y., Frieder, O.: Sparse power efficient topology for wireless networks. In: IEEE Hawaii Int. Conf. on System Sciences (HICSS), Big Island, 7–10 January 2002Google Scholar
  12. 12.
    Li, X.-Y., Wang, Y., Song, W.-Z., Wan, P.-J., Frieder, O.: Localized minimum spanning tree and its applications in wireless ad hoc networks. In: IEEE INFOCOM, Hong Kong, 7–11 March 2004Google Scholar
  13. 13.
    Song, W.-Z., Wang, Y., Li, X.-Y. Frieder, O.: Localized algorithms for energy efficient topology in wireless ad hoc networks. In: ACM Int. Symposium on Mobile Ad-Hoc Networking and Computing (MobiHoc), Tokyo, 24–26 May 2004Google Scholar
  14. 14.
    Toussaint, G.T.: The relative neighborhood graph of a finite planar set. Pattern Recognit. 12(4), 261–268 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Wan, P.-J., Calinescu, G., Li, X.-Y., Frieder, O.: Minimum‐energy broadcast routing in static ad hoc wireless networks. ACM Wireless Networks (2002), To appear, Preliminary version appeared in IEEE INFOCOM, Anchorage, 22–26 April 2001Google Scholar
  16. 16.
    Wang, Y., Li, X.-Y.: Efficient construction of bounded degree and planar spanner for wireless networks. In: ACM DIALM-POMC Joint Workshop on Foundations of Mobile Computing, San Diego, 19 September 2003Google Scholar
  17. 17.
    Yao, A.C.-C.: On constructing minimum spanning trees in k‑dimensional spaces and related problems. SIAM J. Comput. 11, 721–736 (1982)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Wen-Zhan Song
    • 1
  • Xiang-Yang Li
    • 2
  • Weizhao Wang
    • 3
  1. 1.School of Engineering and Computer ScienceWashington State UniversityVancouverUSA
  2. 2.Department of Computer ScienceIllinois Institute of TechnologyChicagoUSA
  3. 3.Google IncIrvineUSA