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Dynamic Routing and Location Services in Metrics of Low Doubling Dimension

(Extended Abstract)
  • Goran Konjevod
  • Andréa W. Richa
  • Donglin Xia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5218)

Abstract

We consider dynamic compact routing in metrics of low doubling dimension. Given a set of nodes V in a metric space with nodes joining, leaving and moving, we show how to maintain a set of links E that allows compact routing on the graph G(V,E). Given a constant ε ∈ (0,1) and a dynamic node set V with normalized diameter Δ in a metric of doubling dimension Open image in new window , we achieve a dynamic graph G(V,E) with maximum degree 2O(α) log2 Δ, and an optimal (9 + ε)-stretch compact name-independent routing scheme on G with (1/ε)O(α)log4 Δ-bit storage at each node. Moreover, the amortized number of messages for a node joining, leaving and moving is polylogarithmic in the normalized diameter Δ; and the cost (total distance traversed by all messages generated) of a node move operation is proportional to the distance the node has traveled times a polylog factor. (We can also show similar bounds for a (1 + ε)-stretch compact dynamic labeled routing scheme.)

One important application of our scheme is that it also provides a node location scheme for mobile ad-hoc networks with the same characteristics as our name-independent scheme above, namely optimal (9 + ε) stretch for lookup, polylogarithmic storage overhead (and degree) at the nodes, and locality-sensitive node move/join/leave operations. We also show how to extend our dynamic compact routing scheme to address the more general problem of devising locality-sensitive Distributed Hash Tables (DHTs) in dynamic networks of low doubling dimension. Our proposed DHT scheme also has optimal (9 + ε) stretch, polylogarithmic storage overhead (and degree) at the nodes, locality-sensitive publish/unpublish and node move/join/leave operations.

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References

  1. 1.
    Abraham, I., Dolev, D., Malkhi, D.: LLS: a locality aware location service for mobile ad hoc networks. In: Proc. 2004 DIALM-POMC (2004)Google Scholar
  2. 2.
    Abraham, I., Gavoille, C., Goldberg, A.V., Malkhi, D.: Routing in networks with low doubling dimension. In: Proc. 26th ICDCS, p. 75 (2006)Google Scholar
  3. 3.
    Abraham, I., Gavoille, C., Malkhi, D.: On space-stretch trade-offs: Lower bounds. In: Proc. 18th SPAA, pp. 207–216 (2006)Google Scholar
  4. 4.
    Abraham, I., Malkhi, D., Dobzinski, O.: Land: stretch (1 + ε) locality-aware networks for DHTs. In: Proc. 15th SODA, pp. 550–559 (2004)Google Scholar
  5. 5.
    Awerbuch, B., Peleg, D.: Online tracking of mobile users. J. ACM 42(5), 1021–1058 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Carter, J.L., Wegman, M.N.: Universal classes of hash functions. J. Comp. Sys. Sci. 18(2), 143–154 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chan, H.T.-H., Gupta, A., Maggs, B.M., Zhou, S.: On hierarchical routing in doubling metrics. In: Proc. 16th SODA, pp. 762–771 (2005)Google Scholar
  8. 8.
    Flury, R., Wattenhofer, R.: MLS: an efficient location service for mobile ad hoc networks. In: Proc. 7th MobiHoc, pp. 226–237 (2006)Google Scholar
  9. 9.
    Gupta, A., Krauthgamer, R., Lee, J.R.: Bounded geometries, fractals and low-distortion embeddings. In: Proc. 44th FOCS, pp. 534–543 (2003)Google Scholar
  10. 10.
    Hildrum, K., Krauthgamer, R., Kubiatowicz, J.: Object location in realistic networks. In: Proc. 16th SPAA, pp. 25–35 (2004)Google Scholar
  11. 11.
    Konjevod, G., Richa, A.W., Xia, D.: Optimal-stretch name-independent compact routing in doubling metrics. In: Proc. 25th PODC, pp. 198–207 (2006)Google Scholar
  12. 12.
    Konjevod, G., Richa, A.W., Xia, D.: Optimal scale-free compact routing schemes in networks of low doubling dimension. In: Proc. 18th SODA, pp. 939–948 (2007)Google Scholar
  13. 13.
    Konjevod, G., Richa, A.W., Xia, D.: Dynamic routing and location services in metrics of low doubling dimension. Technical report, ASU (2008), http://thrackle.eas.asu.edu/users/goran/papers/dynamic-routing.pdf
  14. 14.
    Konjevod, G., Richa, A.W., Xia, D., Yu, H.: Compact routing with slack in low doubling dimension. In: Proc. 26th PODC, pp. 71–80 (2007)Google Scholar
  15. 15.
    Korman, A., Peleg, D.: Dynamic routing schemes for general graphs. In: Proc. 33rd ICALP, pp. 619–630 (2006)Google Scholar
  16. 16.
    Plaxton, C.G., Rajaraman, R., Richa, A.W.: Accessing nearby copies of replicated objects in a distributed environment. In: Proc. 9th SPAA, pp. 311–320 (1997)Google Scholar
  17. 17.
    Ratnasamy, S., Francis, P., Handley, M., Karp, R., Shenker, S.: A scalable Content-Addressable network. In: Proc. 2001 SIGCOMM, pp. 161–172 (2001)Google Scholar
  18. 18.
    Rowstron, A., Druschel, P.: Pastry: scalable, decentraized object location and routing for large-scale peer-to-peer systems. In: Proc. 18th Middleware (2001)Google Scholar
  19. 19.
    Slivkins, A.: Distance estimation and object location via rings of neighbors. In: Proc. 24th PODC, pp. 41–50 (2005)Google Scholar
  20. 20.
    Slivkins, A.: Towards fast decentralized construction of locality-aware overlay networks. In: Proc. 26th PODC, pp. 89–98 (2007)Google Scholar
  21. 21.
    Stoica, I., Morris, R., Karger, D., Kaashoek, F., Balakrishnan, H.: Chord: A scalable peer-to-peer lookup service for internet applications. In: Proc. 2001 SIGCOMM, pp. 149–160 (2001)Google Scholar
  22. 22.
    Talwar, K.: Bypassing the embedding: algorithms for low dimensional metrics. In: Proc. 36th STOC, pp. 281–290 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Goran Konjevod
    • 1
  • Andréa W. Richa
    • 1
  • Donglin Xia
    • 1
  1. 1.Arizona State UniversityTempeUSA

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