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Compact Routing for Graphs Excluding a Fixed Minor

Extended Abstract
  • Ittai Abraham
  • Cyril Gavoille
  • Dahlia Malkhi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3724)

Abstract

This paper concerns compact routing schemes with arbitrary node names. We present a compact name-independent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routing tables with poly-logarithmic number of bits at each node.

For shortest-path labeled routing scheme in planar graphs, we prove an Ω(n ε ) space lower bound for some constant ε > 0. This lower bound holds even for bounded degree triangulations, and is optimal for polynomially weighted planar graphs (ε=1/2).

Keywords

Virtual Node Node Label Super Node Stretch Factor Distance Label 
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., Gavoille, C., Malkhi, D.: Routing with improved communication-space trade-off. In: Guerraoui, R. (ed.) DISC 2004. LNCS, vol. 3274, pp. 305–319. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Abraham, I., Gavoille, C., Malkhi, D.: Routing with improved communication-space trade-off. Tech. Report RR-1330-04, LaBRI, University of Bordeaux 1, 351, cours de la Liberation, 33405 Talence Cedex, France (July 2004)Google Scholar
  3. 3.
    Abraham, I., Gavoille, C., Malkhi, D., Nisan, N., Thorup, M.: Compact name-independent routing with minimum stretch. In: 16th Annual ACM Symposium on Parallel Algorithms and Architecture (SPAA). ACM PRESS, New York (2004)Google Scholar
  4. 4.
    Abraham, I., Malkhi, D.: Compact routing on euclidian metrics. In: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing (PODC), pp. 141–149. ACM Press, New York (2004)CrossRefGoogle Scholar
  5. 5.
    Abraham, I., Malkhi, D.: Name independent routing for growth bounded networks. In: 17th Annual ACM Symposium on Parallel Algorithms and Architecture (SPAA), ACM Press, New York (2005) (to appear)Google Scholar
  6. 6.
    Awerbuch, B., Peleg, D.: Sparse partitions. In: 31st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 503–513. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  7. 7.
    Awerbuch, B., Peleg, D.: Routing with polynomial communication-space trade-off. SIAM J. Discret. Math. 5, 151–162 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bose, P., Morin, P.: Competitive online routing in geometric graphs. Theoretical Computer Science 324, 273–288 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bose, P., Morin, P.: Online routing in triangulations. SIAM Journal on Computing 33, 937–951 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Chan, H.T.-H., Gupta, A., Maggs, B.M., Zhou, S.: On hierarchical routing in doubling metrics. In: 16th Symposium on Discrete Algorithms (SODA), January 2005. ACM/SIAM (2005)Google Scholar
  11. 11.
    Chepoi, V.D., Dragan, F.F., Vaxes, Y.: Distance and routing labeling schemes for non-positively curved plane graphs. Journal of Algorithms (2004) (to appear)Google Scholar
  12. 12.
    Chepoi, V.D., Rollin, A.: Interval routing in some planar quadrangulations. In: 8th International Colloquium on Structural Information & Communication Complexity (SIROCCO), June 2001, pp. 89–104. Carleton Scientific (2001)Google Scholar
  13. 13.
    DeVos, M., Ding, G., Oporowski, B., Sanders, D.P., Reed, B., Seymour, P.D., Vertigan, D.: Excluding any graph as a minor allows a low tree-width 2-coloring. Journal of Combinatorial Theory, Series B 91, 25–41 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Dourisboure, Y.: Compact routing schemes for bounded tree-length graphs and for k-chordal graphs. In: Guerraoui, R. (ed.) DISC 2004. LNCS, vol. 3274, pp. 365–378. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Dourisboure, Y., Gavoille, C.: Improved compact routing scheme for chordal graphs. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 252–264. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Dragan, F.F., Lomonosov, I.: On compact and efficient routing in certain graph classes. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 402–414. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Eilam, T., Gavoille, C., Peleg, D.: Compact routing schemes with low stretch factor. Journal of Algorithms 46, 97–114 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Flocchini, P., Luccio, F.L.: Routing in series parallel networks. Theory Comput. Syst. 36, 137–157 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Frederickson, G.N., Janardan, R.: Efficient message routing in planar networks. SIAM Journal on Computing 18, 843–857 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Gavoille, C.: Routing in distributed networks: Overview and open problems. ACM SIGACT News - Distributed Computing Column 32, 36–52 (2001)CrossRefGoogle Scholar
  21. 21.
    Gavoille, C., Hanusse, N.: Compact routing tables for graphs of bounded genus. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 351–360. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Journal of Distributed Computing 16, 111–120 (2003) PODC 20-Year Issue CrossRefGoogle Scholar
  23. 23.
    Gavoille, C., Peleg, D., Pérennès, S., Raz, R.: Distance labeling in graphs. Journal of Algorithms 53, 85–112 (2004)zbMATHCrossRefGoogle Scholar
  24. 24.
    Gupta, A., Krauthgamer, R., Lee, J.R.: Bounded geometries, fractals, and low-distortion embeddings. In: 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 534–543. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar
  25. 25.
    Hassin, Y., Peleg, D.: Sparse communication networks and efficient routing in the plane. Distributed Computing 14, 205–215 (2001)CrossRefGoogle Scholar
  26. 26.
    Klein, P., Plotkin, S.A., Rao, S.: Excluded minors, network decomposition, and multicommodity flow. In: 25th Annual ACM Symposium on Theory of Computing (STOC), pp. 682–690. ACM Press, New York (1993)Google Scholar
  27. 27.
    Laing, K.A.: Brief announcement: name-independent compact routing in trees. In: 24th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 382–382. ACM Press, New York (2004)Google Scholar
  28. 28.
    Lu, H.-I.: Improved compact routing tables for planar networks via orderly spanning trees. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 57–66. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  29. 29.
    Nash-Williams, C.S.J.: Edge-disjoint spanning trees of finite graphs. J. London Math. Soc. 36, 445–450 (1961)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications (2000)Google Scholar
  31. 31.
    Peleg, D.: Proximity-preserving labeling schemes. Journal of Graph Theory 33, 167–176 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Peleg, D., Upfal, E.: A trade-off between space and efficiency for routing tables. Journal of the ACM 36, 510–530 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Slivkins, A.: Distance estimation and object location via rings of neighbors. In: 24th Annual ACM Symposium on Principles of Distributed Computing (PODC). ACM Press, New York (2005) (to appear), Also appears as Cornell CIS technical report TR2005-1977Google Scholar
  34. 34.
    Talwar, K.: Bypassing the embedding: Algorithms for low dimensional metrics. In: 36th Annual ACM Symposium on Theory of Computing (STOC), June 2004, pp. 281–290 (2004)Google Scholar
  35. 35.
    Thorup, M.: Compact oracles for reachability and approximate distances in planar digraphs. In: 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 242–251. IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
  36. 36.
    Thorup, M., Zwick, U.: Compact routing schemes. In: 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), pp. 1–10. ACM Press, New York (2001)Google Scholar
  37. 37.
    West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Englewood Cliffs (2001)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ittai Abraham
    • 1
  • Cyril Gavoille
    • 2
  • Dahlia Malkhi
    • 1
    • 3
  1. 1.School of Computer Science and EngineeringThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Laboratoire Bordelais de Recherche en InformatiqueUniversity of BordeauxBordeauxFrance
  3. 3.Silicon Valley CenterMicrosoft Research 

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