Geometric Routing Without Geometry

  • Mirjam Wattenhofer
  • Roger Wattenhofer
  • Peter Widmayer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3499)

Abstract

In this paper we propose a new routing paradigm, called pseudo-geometric routing. In pseudo-geometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On theses pseudo coordinates we employ greedy geometric routing. Almost as a side effect, pseudo-geometric routing is not restricted to planar unit disk graph networks anymore, but succeeds on general networks.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abraham, I., Dolev, D., Malkhi, D.: LLS: a Locality Aware Location Service for Mobile Ad hoc Networks. In: Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, DIAL-M (2004)Google Scholar
  2. 2.
    Abraham, I., Gavoille, C., Malkhi, D., Nisan, N., Thorup, M.: Compact Name Independent Routing with Minimum Stretch. In: Proc. of the ACM Symposium on Parallelism in Algorithms and Architectures, SPAA (2004)Google Scholar
  3. 3.
    Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with Guaranteed Delivery in Ad hoc Wireless Networks. In: Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, DIAL-M (1999)Google Scholar
  4. 4.
    Busch, C., Surapaneni, S., Tirthapura, S.: Analysis of Link Reversal Routing Algorithms for Mobile Ad hoc Networks. In: SPAA 2003: Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures, pp. 210–219. ACM Press, New York (2003)CrossRefGoogle Scholar
  5. 5.
    Cowen, L.: Compact Routing with Minimum Stretch. In: Proc. of the ACM-SIAM Symp. on Discrete Algorithms, SODA (1999)Google Scholar
  6. 6.
    Doherty, L., Ghaoui, L.E., Pister, K.: Convex Position Estimation in Wireless Sensor Networks. In: Proc. of Joint Conf. of the IEEE Computer and Communications Societies, INFOCOM (2001)Google Scholar
  7. 7.
    Eilam, T., Moran, S., Zaks, S.: A Simple DFS-Based Algorithm for Linear Interval Routing. In: WDAG 1997: Proceedings of the 11th International Workshop on Distributed Algorithms (1997)Google Scholar
  8. 8.
    Fath, K., Flocchini, P., Pierre, S.: A Compact Routing Technique for Communication Networks. In: IEEE Canadian Conference on Electrical and Computer Engineering (1999)Google Scholar
  9. 9.
    Fraigniaud, P., Gavoille, C.: Interval Routing Schemes. Algorithmica 21(2), 155–182 (1998)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fraigniaud, P., Gavoille, C., Mans, B.: Interval Routing Schemes Allow Broadcasting with Linear Message-complexity. In: Proc. of Symp. on Principles of Distributed Computing (PODC)Google Scholar
  11. 11.
    Gafni, E.M., Bertsekas, D.P.: Distributed algorithms for Generating Loop-free Routes in Networks with Frequently Changing Topology. IEEE Transactions on Communications 29, 11–18 (1981)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Gavoille, C.: A Survey on Interval Routing. Theoretical Computer Science 245(2), 217–253 (2000)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Gavoille, C.: Routing in Distributed Networks: Overview and Open Problems. In: SIGACTN: SIGACT News (ACM Special Interest Group on Automata and Computability Theory), vol. 32 (2001)Google Scholar
  14. 14.
    Gavoille, C., Gengler, M.: Space-Efficiency for Routing Schemes of Stretch Factor Three. Journal of Parallel and Distributed Computing 61(5), 679–687 (2001)MATHCrossRefGoogle Scholar
  15. 15.
    Gavoille, C., Peleg, D.: Compact and Localized Distributed Data Structures. Journal of Distributed Computing 16, 111–120Google Scholar
  16. 16.
    Kleinrock, L., Kamoun, F.: Hierarchical Routing for Large Networks. Computer Networks 1, 155–174 (1975)MathSciNetGoogle Scholar
  17. 17.
    Kranakis, E., Singh, H., Urrutia, J.: Compass Routing on Geometric Networks. In: 11th Canadian Conference on Computational Geometry, pp. 51–54 (1999)Google Scholar
  18. 18.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: Unit Disk Graph Approximation. In: Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, DIAL-M (2004)Google Scholar
  19. 19.
    Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric Ad-Hoc Routing: of Theory and Practice. In: Proc. of Symp. on Principles of Distributed Computing, PODC (2003)Google Scholar
  20. 20.
    Moscibroda, T., O’Dell, R., Wattenhofer, M., Wattenhofer, R.: Virtual Coordinates for Ad hoc and Sensor Networks. In: Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, DIAL-M (2004)Google Scholar
  21. 21.
    Peleg, D., Upfal, E.: A Tradeoff between Space and Efficiency for Routing Tables. In: Proc. of ACM Symp. on Theory of Computing, STOC (1988)Google Scholar
  22. 22.
    Rao, A., Papadimitriou, C., Ratnasamy, S., Shenker, S., Stoica, I.: Geographic Routing without Location Information. In: Proc. of Mobile Computing and Networking, MobiCom (2003)Google Scholar
  23. 23.
    Santoro, N., Khatib, R.: Labelling and Implicit Routing in Networks. Comput. J. 28(1), 5–8 (1985)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Shang, Y., Ruml, W., Zhang, Y., Fromherz, M.: Localization from Mere Connectivity. In: Proc. of Intl. Symp. on Mobile Ad Hoc Networking and Computing (MobiHoc) (2003)Google Scholar
  25. 25.
    Takagi, H., Kleinrock, L.: Optimal Transmission Ranges for Randomly dDistributed Packet Radio Terminals. IEEE Transactions on Communications 32, 246–257 (1984)CrossRefGoogle Scholar
  26. 26.
    Thorup, M., Zwick, U.: Compact Routing Schemes. In: Proc. of the ACM Symposium on Parallelism in Algorithms and Architectures, SPAA (2001)Google Scholar
  27. 27.
    van Leeuwen, J., Tan, R.: Interval Routing. The Computer Journal 30, 298–307 (1987)MATHCrossRefGoogle Scholar
  28. 28.
    Wattenhofer, M., Wattenhofer, R., Widmayer, P.: Geometric routing without geometry. Technical report, ETH Zurich (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Mirjam Wattenhofer
    • 1
  • Roger Wattenhofer
    • 2
  • Peter Widmayer
    • 1
  1. 1.Department of Computer ScienceETH Zurich 
  2. 2.Computer Engineering and Networks LaboratoryETH Zurich 

Personalised recommendations