Optimal layouts on a chain ATM network

Extended abstract
  • Ornan Gerstel
  • Avishai Wool
  • Shmuel Zaks
Session 9. Chair: Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 979)


We study a routing problem which occurs in high-speed (ATM) networks, termed the “one-to-many virtual path layout problem” on chain networks. This problem is essentially a tree embedding problem on a chain host graph. We present four performance measures to the quality of such an embedding which have practical implications, and find optimal solutions for each of them. We first show that the search can be restricted to the class of layouts with no crossovers. Given bounds on the load ℓ and number of hops h in a layout, we then present a family of ordered trees \(\mathcal{T}\)(l, h), within which an optimal solution can be found (if one exists at all); this holds for either the worst-case or average-case measures, and for a chain of length n, with n\(\left( {\begin{array}{*{20}c}{l + h} \\l \\\end{array} } \right)\). For the worstcase measures these trees are used in characterizing, constructing, and proving the optimality of the solutions. For the average-case measures polynomial dynamic programming algorithms are presented which find optimal solutions for all cases.


Dynamic Programming Algorithm Chain Network Layout Problem Optimal Layout Weight Assignment 
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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  1. [ABNLP89]
    B. Awerbuch, A. Bar-Noy, N. Linial, and D. Peleg. Compact distributed data structures for adaptive routing. In 21st Symp. on Theory of Computing, pages 479–489, 1989.Google Scholar
  2. [AP92]
    B. Awerbuch and D. Peleg. Routing with polynomial communicationspace tradeoff. SIAM Journal on Discrete Math, 5(2):151–162, May 1992.CrossRefGoogle Scholar
  3. [ATTD94]
    S. Ahn, R.P. Tsang, S.R. Tong, and D.H.C. Du. Virtual path layout design on ATM networks. In IEEE Infocom'94, pages 192–200, 1994.Google Scholar
  4. [BTS94]
    H.L. Bodlaender, G. Tel, and N. Santoro. Trade-offs in non-reversing diameter. Nordic Journal of Computing, 1:111–134, 1994.Google Scholar
  5. [CGZ94]
    I. Cidon, O. Gerstel, and S. Zaks. A scalable approach to routing in ATM networks. In G. Tel and P.M.B. Vitányi, editors, The 8th International Workshop on Distributed Algorithms (LNCS 857), pages 209–222, Terschelling, The Netherlands, October 1994.Google Scholar
  6. [CLR89]
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, 1989.Google Scholar
  7. [CS94]
    R. Cohen and A. Segall. Connection management and rerouting in ATM networks. In IEEE Infocom'94, pages 184–191, 1994.Google Scholar
  8. [FJ86]
    G.N. Frederickson and R. Janardan. Separator-based strategies for efficient message routing. In 27th Symp. on Foundations of Computer Science, pages 428–437, 1986.Google Scholar
  9. [GKP89]
    R. L. Graham, D. E. Knuth, and O. Patashnik. Concrete Mathematics. Addison-Wesley, 1989.Google Scholar
  10. [GS95]
    O. Gerstel and A. Segall. Dynamic maintenance of the virtual path layout. In IEEE Infocom'95, pages 330–337, April 1995.Google Scholar
  11. [GZ94]
    O. Gerstel and S. Zaks. The virtual path layout problem in fast networks. In The 13th ACM Symp. on Principles of Distributed Computing, pages 235–243, Los Angeles, USA, August 1994.Google Scholar
  12. [HH91]
    R. Händler and M.N. Huber. Integrated Broadband Networks: an introduction to ATM-based networks. Addison-Wesley, 1991.Google Scholar
  13. [ITU90]
    ITU recommendation. I series (B-ISDN), Blue Book, November 1990.Google Scholar
  14. [KK80]
    L. Kleinrock and F. Kamoun. Optimal clustering structures for hierarchical topological design of large computer networks. Networks, 10:221–248, 1980.Google Scholar
  15. [LC93]
    F.Y.S. Lin and K.T. Cheng. Virtual path assignment and virtual circuit routing in ATM networks. In IEEE Globecom '93, pages 436–441, 1993.Google Scholar
  16. [PU88]
    D. Peleg and E. Upfal. A tradeoff between space and efficiency for routing tables. In 20th Symp. on Theory of Computing, pages 43–52, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Ornan Gerstel
    • 1
  • Avishai Wool
    • 2
  • Shmuel Zaks
    • 1
  1. 1.Department of Computer ScienceTechnionHaifaIsrael
  2. 2.Department of Applied Mathematics and Computer ScienceThe Weizmann InstituteRehovotIsrael

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