Routing in Trees

  • Pierre Fraigniaud
  • Cyril Gavoille
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)

Abstract

This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that n-node trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing decision is taken in constant time. This improves the best known routing scheme by a factor of O(log n) in term of both memory requirements and routing time. Our routing scheme requires headers and addresses of size slightly larger than log n, motivated by an inherent trade-off between address-size and memory space, i.e., any routing scheme with addresses on log n bits requires Ω(√n) bits of local memory-space. This shows that a little variation of the address size, e.g., by an additive O(log n) bits factor, has a significant impact on the local memory space.

Keywords

compact routing trees routing algorithms 

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References

  1. 1.
    B. Awerbuch AND D. Peleg, Sparse partitions, in 31th Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, 1990, pp. 503–513.Google Scholar
  2. 2.
    L. J. Cowen, Compact routing with minimum stretch, in 10th Symposium on Discrete Algorithms (SODA), ACM-SIAM, 1999, pp. 255–260.Google Scholar
  3. 3.
    T. Eilam, C. Gavoille, AND D. Peleg, Compact routing schemes with low stretch factor, in 17th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM PRESS, Aug. 1998, pp. 11–20.Google Scholar
  4. 4.
    C. Gavoille, A survey on interval routing, Theoretical Computer Science, 245 (2000), pp. 217–253.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    C. Gavoille AND S. Pérennès, Memory requirement for routing in distributed networks, in 15th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM PRESS, May 1996, pp. 125–133.Google Scholar
  6. 6.
    M. J. Hall, Combinatorial Theory (second edition), Wiley-Interscience Publication, 1986.Google Scholar
  7. 7.
    J. I. Munro, Tables, in 16th FST&TCS, vol. 1180 of Lectures Notes in Computer Science, Springer-Verlag, 1996, pp. 37–42.Google Scholar
  8. 8.
    J. I. Munro AND V. Raman, Succinct representation of balanced parentheses, static trees and planar graphs, in 38th Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, Oct. 1997, pp. 118–126.Google Scholar
  9. 9.
    D. Peleg, Proximity-preserving labeling schemes and their applications, in 25th International Workshop, Graph-Theoretic Concepts in Computer Science (WG), vol. 1665 of Lecture Notes in Computer Science, Springer, June 1999, pp. 30–41.CrossRefGoogle Scholar
  10. 10.
    D. Peleg AND E. Upfal, A trade-off between space and efficiency for routing tables, Journal of the ACM, 36 (1989), pp. 510–530.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    N. Santoro AND R. Khatib, Labelling and implicit routing in networks, The Computer Journal, 28 (1985), pp. 5–8.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    M. Thorup AND U. Zwick, Compact routing schemes, in 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), ACM PRESS, July 2001. To appear.Google Scholar
  13. 13.
    J. VAN Leeuwen AND R. B. Ttan, Interval routing, The Computer Journal, 30 (1987), pp. 298–307.MATHCrossRefGoogle Scholar
  14. 14.
    R. Warlimont, Factorisatio numerorum with constraints, Journal of Number Theory, 45 (1993), pp. 186–199.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Pierre Fraigniaud
    • 1
  • Cyril Gavoille
    • 2
  1. 1.CNRS, Laboratoire de Recherche en InformatiqueUniversité Paris-SudOrsayFrance
  2. 2.Laboratoire Bordelais de Recherche en InformatiqueUniversité Bordeaux ITalenceFrance

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