Directed virtual path layouts in ATM networks

Extended abstract
  • Jean-Claude Bermond
  • Nausica Marlin
  • David Peleg
  • Stéphane Perennes
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1499)


This article investigates the problem of designing virtual dipaths (VPs) in a directed ATM model, in which the flow of information in the two directions of a link are not identical. On top of a given physical network we construct directed VPs. Routing in the physical network is done using these VPs. Given the capacity of each physical link (the maximum number of VPs that can pass through the link) the problem consists in defining a set of VPs to minimize the diameter of the virtual network formed by these VPs (the maximum number of VPs traversed by any single message). For the most popular types of simple networks, namely the path, the cycle, the grid, the tori, the complete k-ary tree, and the general tree, we present optimal or near optimal lower and upper bounds on the virtual diameter as a function of the capacity.


ATM Virtual path layout diameter Embedding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Becchetti, P. Bertolazzi, C. Gaibisso, and G. Gambosi. On the design of efficient ATM routing schemes. manuscript, 1997.Google Scholar
  2. 2.
    J.-C. Bermond, L. Gargano, S. Perennes, A. Rescigno, and U. Vaccaro. Effective collective communication in optical networks. In Proceedings of ICALP 96, volume 1099 of Lectures Notes In Computer Science, pages 574–585. Springer Verlag, July 1996.Google Scholar
  3. 3.
    M. Burlet, P. Chanas, and O. Goldschmidt. Optimization of VP layout in ATM networks. In preparation, 1998.Google Scholar
  4. 4.
    P. Chanas. Dimensionnement de réseaux ATM. PhD thesis, CNET Sophia, Sept. 1998. In preparation.Google Scholar
  5. 5.
    P. Chanas and O. Goldschmidt. Conception de réseau de VP de diamètre minimum pour les réseaux ATM. In Road-f'98, pages 38–40, 1998.Google Scholar
  6. 6.
    M. De Pricker. Asynchronous Transfer Mode, Solution for Broadband ISDN. Prentice Hall, August 1995. 3rd edition 332p.Google Scholar
  7. 7.
    O. Delmas and S. Perennes. Circuit-Switched Gossiping in 3-Dimensional Torus Networks. In Proc. Euro-Par'96 Parallel Processing/2nd Int. EURO-PAR Conference, volume 1123 of Lecture Notes in Computer Science, pages 370–373, Lyon, France, Aug. 1996. Springer Verlag.Google Scholar
  8. 8.
    T. Eilam, M. Flammini, and S. Zaks. A complete characterization of the path layout construction problem for ATM networks with given hop count and load. In 24th International Colloquium on Automata, Languages and Programming (ICALP), volume 1256 of Lecture Notes in Computer Science, pages 527–537. Springer-Verlag, 1997.Google Scholar
  9. 9.
    M. Feighlstein and S. Zaks. Duality in chain ATM virtual path layouts. In 4th International Colloquium on Structural Information and Communication Complexity (SIROCCO), Monte Verita, Ascona, Switzerland, July 1997.Google Scholar
  10. 10.
    O. Gerstel, I. Cidon, and S. Zaks. The layout of virtual paths in ATM networks. IEEE/ACM Transactions on Networking, 4(6):873–884, 1996.CrossRefGoogle Scholar
  11. 11.
    O. Gerstel, A. Wool, and S. Zaks. Optimal layouts on a chain ATM network. In 3rd Annual European Symposium on Algorithms, volume LNCS 979, pages 508–522. Springer Verlag, 1995.Google Scholar
  12. 12.
    O. Gerstel and S. Zaks. The virtual path layout problem in fast networks. In Symposium on Principles of Distributed Computing (PODC '94), pages 235–243, New York, USA, Aug. 1994. ACM Press.Google Scholar
  13. 13.
    M.-C. Heydemann, J.-C. Meyer, and D. Sotteau. On forwarding indices of networks. Discrete Appl. Math., 23:103–123, 1989.MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    J.-W. Hong, K. Mehlhorn, and A. Rosenberg. Cost trade-offs in graph embeddings, with applications. J. ACM, 30:709–728, 1983.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Kofman and M. Gagnaire. Réseaux Haut Débit, réseaux ATM, réseaux locaux et réseaux tout-optiques. InterEditions-Masson, 1998. 2eme édition.Google Scholar
  16. 16.
    E. Kranakis, D. Krizanc, and A. Pelc. Hop-congestion trade-offs for high-speed networks. International Journal of Foundations of Computer Science, 8:117–126, 1997.MATHCrossRefGoogle Scholar
  17. 17.
    Y. Manoussakis and Z. Tuza. The forwarding index of directed networks. Discrete Appl. Math., 68:279–291, 1996.MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    A. Rosenberg. Issues in the study of graph embeddings. In Graph-Theoretic concepts in computer science. Springer, 1980.Google Scholar
  19. 19.
    P. Solé. Expanding and forwarding. Discrete Appl. Math., 58:67–78, 1995.MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    L. Stacho and I. Vrt'o. Virtual path layouts for some bounded degree networks. In Structure, Information and Communication Complexity, 3rd Colloquium, SIROCCO, pages 269–278. Carleton University Press, 1996.Google Scholar
  21. 21.
    S. Zaks. Path layout in ATM networks — a survey. In The DIMACS Workshop on Networks in Distributed Computing, DIMACS Center, Rutgers University, Oct. 1997. manuscript.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jean-Claude Bermond
    • 1
  • Nausica Marlin
    • 2
  • David Peleg
    • 3
  • Stéphane Perennes
    • 4
  1. 1.SLOOP joint project CNRS-UNSA-INRIAI3S Université de NiceSophia-AntipolisFrance
  2. 2.SLOOP joint project CNRS-UNSA-INRIAI3S Université de NiceSophia-AntipolisFrance
  3. 3.Department of Applied Mathematics and Computer ScienceThe Weizmann InstituteRehovotIsrael
  4. 4.SLOOP joint project CNRS-UNSA-INRIAI3S Université de NiceSophia-AntipolisFrance

Personalised recommendations