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Fault-Tolerant Compact Routing Schemes for General Graphs

  • Shiri Chechik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)

Abstract

This paper considers compact fault-tolerant routing schemes for weighted general graphs, namely, routing schemes that avoid a set of failed (or forbidden) edges. We present a compact routing scheme capable of handling multiple edge failures. Assume a source node s contains a message M designated to a destination target t and assume a set F of edges crashes (unknown to s). Our scheme routes the message to t (provided that s and t are still connected in G ∖ F) over a path whose length is proportional to the distance between s and t in G ∖ F, to |F|3 and to some poly-log factor. The routing table required at a node v is of size proportional to the degree of v in G and some poly-log factor. This improves on the previously known fault-tolerant compact routing scheme for general graphs, which was capable of overcoming at most 2 edge failures.

Keywords

Source Node Search Tree Internal Node General Graph Unweighted 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.

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References

  1. 1.
    Abraham, I., Chechik, S., Gavoille, C., Peleg, D.: Forbidden-set distance labels for graphs of bounded doubling dimension. In: PODC, pp. 192–200 (2010)Google Scholar
  2. 2.
    Alstrup, S., Brodal, G.S., Rauhe, T.: New Data Structures for Orthogonal Range Searching. In: Proc. 41st IEEE Symp. on Foundations of Computer Science (FOCS), pp. 198–207 (2001)Google Scholar
  3. 3.
    Awerbuch, B., Bar-Noy, A., Linial, N., Peleg, D.: Improved routing strategies with succinct tables. J. Algorithms, 307–341 (1990)Google Scholar
  4. 4.
    Awerbuch, B., Kutten, S., Peleg, D.: On buffer-economical store-and-forward deadlock prevention. In: Proc. INFOCOM, pp. 410–414 (1991)Google Scholar
  5. 5.
    Awerbuch, B., Peleg, D.: Sparse partitions. In: 31st FOCS, pp. 503–513 (1990)Google Scholar
  6. 6.
    Chechik, S., Langberg, M., Peleg, D., Roditty, L.: f-sensitivity distance oracles and routing schemes. In: 18th ESA, pp. 84–96 (2010)Google Scholar
  7. 7.
    Cohen, E.: Fast algorithms for constructing t-spanners and paths with stretch t. In: Proc. IEEE Symp. on Foundations of Computer Science, pp. 648–658 (1993)Google Scholar
  8. 8.
    Courcelle, B., Twigg, A.: Compact forbidden-set routing. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 37–48. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Cowen, L.J.: Compact routing with minimum stretch. J. Alg. 38, 170–183 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  11. 11.
    Duan, R., Pettie, S.: Connectivity oracles for failure prone graphs. In: Proc. ACM STOC (2010)Google Scholar
  12. 12.
    Eilam, T., Gavoille, C., Peleg, D.: Compact routing schemes with low stretch factor. J. Algorithms 46, 97–114 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Fraigniaud, P., Gavoille, C.: Memory requirement for universal routing schemes. In: 14th PODC, pp. 223–230 (1995)Google Scholar
  14. 14.
    Gavoille, C., Gengler, M.: Space-efficiency for routing schemes of stretch factor three. J. Parallel Distrib. Comput. 61, 679–687 (2001)CrossRefzbMATHGoogle Scholar
  15. 15.
    Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Distributed Computing 16, 111–120 (2003)CrossRefGoogle Scholar
  16. 16.
    Peleg, D.: Distributed computing: a locality-sensitive approach. SIAM, Philadelphia (2000)CrossRefzbMATHGoogle Scholar
  17. 17.
    Peleg, D., Upfal, E.: A trade-off between space and efficiency for routing tables. J. ACM 36(3), 510–530 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Thorup, M., Zwick, U.: Compact routing schemes. In: Proc. 13th ACM Symp. on Parallel Algorithms and Architectures (SPAA), pp. 1–10 (2001)Google Scholar
  19. 19.
    Thorup, M., Zwick, U.: Approximate distance oracles. J. ACM 52, 1–24 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Twigg, D.A.: Forbidden-set Routing. PhD thesis, University of Cambridge, King’s College (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shiri Chechik
    • 1
  1. 1.Department of Computer Science and Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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