Distributed Proximity Maintenance in Ad Hoc Mobile Networks

  • Jie Gao
  • Leonidas J. Guibas
  • An Nguyen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3560)


We present an efficient distributed data structure, called the d-Spanner, for maintaining proximity information among communicating mobile nodes. The d-Spanner is a kinetic sparse graph spanner on the nodes that allows each node to quickly determine which other nodes are within a given distance of itself, to estimate an approximate nearest neighbor, and to perform a variety of other proximity related tasks. A lightweight and fully distributed implementation is possible, in that maintenance of the proximity information only requires each node to exchange a modest number of messages with a small number of mostly neighboring nodes. The structure is based on distance information between communicating nodes that can be derived using ranging or localization methods and requires no additional shared infrastructure other than an underlying communication network. Its modest requirements make it scalable to networks with large numbers of nodes.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agarwal, P., Basch, J., Guibas, L., Hershberger, J., Zhang, L.: Deformable free space tilings for kinetic collision detection. International Journal of Robotics Research 21(3), 179–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Amir, A., Efrat, A., Myllymaki, J., Palaniappan, L., Wampler, K.: Buddy tracking - efficient proximity detection among mobile friends. In: Proc. of the 23rd Conference of the IEEE Communications Society (INFOCOM), March 2004, vol. 23, pp. 298–309 (2004)Google Scholar
  3. 3.
    Basch, J., Erickson, J., Guibas, L.J., Hershberger, J., Zhang, L.: Kinetic collision detection between two simple polygons. In: Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, pp. 102–111 (1999)Google Scholar
  4. 4.
    Basch, J., Guibas, L., Hershberger, J.: Data structures for mobile data. J. Alg. 31(1), 1–28 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Basch, J., Guibas, L.J., Zhang, L.: Proximity problems on moving points. In: Proc. 13th Annu. ACM Sympos. Comput. Geom., pp. 344–351 (1997)Google Scholar
  6. 6.
    Basu, A., Boshes, B., Mukherjee, S., Ramanathan, S.: Network deformation: traffic-aware algorithms for dynamically reducing end-to-end delay in multi-hop wireless networks. In: Proceedings of the 10th annual international conference on Mobile computing and networking, pp. 100–113. ACM Press, New York (2004)CrossRefGoogle Scholar
  7. 7.
    Callahan, P.B., Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. J. ACM 42, 67–90 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Eppstein, D.: Spanning trees and spanners. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 425–461. Elsevier Science Publishers B.V, North-Holland (2000)CrossRefGoogle Scholar
  9. 9.
    Gao, J., Guibas, L., Hershberger, J., Zhang, L., Zhu, A.: Discrete mobile centers. Discrete and Computational Geometry 30(1), 45–63 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gao, J., Guibas, L., Nguyen, A.: Deformable spanners and applications. In: Proc. ACM Symposium on Computational Geometry, June 2004, pp. 190–199 (2004)Google Scholar
  11. 11.
    Gao, J., Guibas, L.J., Nguyen, A.: Distributed proximity maintenance in ad hoc mobile networks (2005),
  12. 12.
    Guibas, L., Hershberger, J., Suri, S., Zhang, L.: Kinetic connectivity for unit disks. In: Proc. 16th Annu. ACM Sympos. Comput. Geom., pp. 331–340 (2000)Google Scholar
  13. 13.
    Guibas, L., Nguyen, A., Russel, D., Zhang, L.: Collision detection for deforming necklaces. In: Proc. 18th ACM Symposium on Computational Geometry, pp. 33–42 (2002)Google Scholar
  14. 14.
    Guibas, L.J.: Kinetic data structures — a state of the art report. In: Agarwal, P.K., Kavraki, L.E., Mason, M. (eds.) Proc. Workshop Algorithmic Found. Robot, pp. 191–209. A. K. Peters, Wellesley (1998)Google Scholar
  15. 15.
    Howard, A., Matarić, M.J., Sukhatme, G.S.: An incremental self-deployment algorithm for mobile sensor networks. Autonomous Robots Special Issue on Intelligent Embedded Systems 13(2), 113–126 (2002)zbMATHGoogle Scholar
  16. 16.
    Kaiser, W.J., Pottie, G.J., Srivastava, M., Sukhatme, G.S., Villasenor, J., Estrin, D.: Networked infomechanical systems (NIMS) for ambient intelligence. CENS Technical Report 31, UCLA (December 2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jie Gao
    • 1
  • Leonidas J. Guibas
    • 2
  • An Nguyen
    • 2
  1. 1.Center for the Mathematics of InformationCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

Personalised recommendations