Online Multi-path Routing in a Maze | SpringerLink
Skip to main content
Springer Nature Link
Log in

Online Multi-path Routing in a Maze

  • Conference paper
Algorithms and Computation (ISAAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4288))

Included in the following conference series:

Abstract

We consider the problem of route discovery in a mesh network with faulty nodes. The number and the positions of the faulty nodes are unknown. It is known that a flooding strategy like expanding ring search can route a message linear in the minimum number of steps d while it causes a traffic (i.e. the total number of messages) of \({\mathcal O}(d^2)\). For optimizing traffic a single-path strategy is optimal producing traffic \({\mathcal O}(d+p)\), where p is the number of nodes that are adjacent to faulty nodes. We present a deterministic multi-path online routing algorithm that delivers a message within \({\mathcal O}(d)\) time steps causing traffic \({\mathcal O}(d + p \log^2 d)\). This algorithm is asymptotically as fast as flooding and nearly traffic-optimal up to a polylogarithmic factor.

Partially supported by the DFG Sonderforschungsbereich 376 and by the EU within 6th Framework Programme under contract 001907 “Dynamically Evolving, Large Scale Information Systems” (DELIS).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Angluin, D., Westbrook, J., Zhu, W.: Robot navigation with distance queries. SIAM Journal on Computing 30(1), 110–144 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Berman, P.: On-line searching and navigation. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms: The State of the Art, pp. 232–241. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  3. Blum, A., Raghavan, P., Schieber, B.: Navigating in unfamiliar geometric terrain. SIAM Journal on Computing 26, 110–137 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  5. Bose, P., Morin, P.: Competitive online routing in geometric graphs. Theoretical Computer Science 324(2-3), 273–288 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bose, P., Morin, P.: Online routing in triangulations. SIAM Journal on Computing 33(4), 937–951 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. Wireless Networks 7(6), 609–616 (2001)

    Article  MATH  Google Scholar 

  8. Cole, R.J., Maggs, B.M., Sitaraman, R.K.: Reconfiguring Arrays with Faults Part I: Worst-case Faults. SIAM Journal on Computing 26(16), 1581–1611 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Johnson, D.B., Maltz, D.A.: Dynamic Source Routing in Ad Hoc Wireless Networks. In: Mobile Computing, pp. 152–181. Kluwer, Dordrecht (1996)

    Google Scholar 

  10. Koutsoupias, E., Papadimitriou, Ch.H.: Beyond competitive analysis. SIAM Journal on Computing 30(1), 300–317 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kranakis, E., Singh, H., Urrutia, J.: Compass routing on geometric networks. In: Proc. 11th Canadian Conference on Computational Geometry, pp. 51–54 (1999)

    Google Scholar 

  12. Kuhn, F., Wattenhofer, R., Zollinger, A.: Asymptotically optimal geometric mobile ad-hoc routing. In: Proc. of the 6th Int. Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 24–33 (2002)

    Google Scholar 

  13. Lucas, C.: Comments on dynamic path planning for a mobile automation with limited information on the environment. IEEE Transactions on Automatic Control 33(5), 511 (1988)

    Article  Google Scholar 

  14. Lumelsky, V.J.: Algorithmic and complexity issues of robot motion in an uncertain environment. J. Complex. 3(2), 146–182 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lumelsky, V.J., Stepanov, A.A.: Path-planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape. Algorithmica 2, 403–430 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mauve, M., Widmer, J., Hartenstein, H.: A survey on position-based routing in mobile ad hoc networks. IEEE Network Magazine 15(6), 30–39 (2001)

    Article  Google Scholar 

  17. Papadimitriou, Ch.H., Yannakakis, M.: Shortest paths without a map. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 610–620. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  18. Perkins, C.E., Belding-Royer, E.M., Das, S.: Ad hoc on-demand distance vector (AODV) routing. IETF RFC 3561 (July 2003)

    Google Scholar 

  19. Rao, N., Kareti, S., Shi, W., Iyenagar, S.: Robot navigation in unknown terrains: Introductory survey of non-heuristic algorithms (1993)

    Google Scholar 

  20. Rührup, S.: Position-based Routing Strategies. PhD thesis, University of Paderborn (2006)

    Google Scholar 

  21. Rührup, S., Schindelhauer, C.: Competitive time and traffic analysis of position-based routing using a cell structure. In: Proc. of the 5th IEEE Int. Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN 2005), p. 248 (2005)

    Google Scholar 

  22. Rührup, S., Schindelhauer, Ch.: Online routing in faulty mesh networks with sub-linear comparative time and traffic ratio. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 23–34. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Rührup, S., Schindelhauer, Ch.: Improved bounds for online multi-path routing in faulty mesh networks. Technical Report TR-RSFB-06-078, University of Paderborn (2006)

    Google Scholar 

  24. Wu, J.: Fault-tolerant adaptive and minimal routing in mesh-connected multicomputers using extended safety levels. IEEE Transactions on Parallel and Distributed Systems 11, 149–159 (2000)

    Article  Google Scholar 

  25. Wu, J., Jiang, Z.: Extended minimal routing in 2-d meshes with faulty blocks. In: Proc. of the 1st Intl. Workshop on Assurance in Distributed Systems and Applications, pp. 49–55 (2002)

    Google Scholar 

  26. Zakrevski, L., Karpovsky, M.: Fault-tolerant message routing for multiprocessors. In: Parallel and Distributed Processing, pp. 714–730. Springer, Heidelberg (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Heinz Nixdorf Institute, University of Paderborn, Germany

    Stefan Rührup

  2. Computer Networks and Telematics, University of Freiburg, Germany

    Christian Schindelhauer

Authors
  1. Stefan Rührup
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Schindelhauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Japan

    Tetsuo Asano

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rührup, S., Schindelhauer, C. (2006). Online Multi-path Routing in a Maze. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_65

Download citation

  • DOI: https://doi.org/10.1007/11940128_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49694-6

  • Online ISBN: 978-3-540-49696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation