Optimal fault-tolerant ATM-routings for biconnected graphs

  • Koichi Wada
  • Wei Chen
  • Yupin Luo
  • Kimio Kawaguchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1335)


We study the problem of designing fault-tolerant virtual path layouts for an ATM network which is a biconnected network of n processors in the surviving route graph model. The surviving route graph for a graph G, a routing p and a set of faults F is a directed graph consisting of nonfaulty nodes with a directed edge from a node x to a node y iff there are no faults on the route from x to y. The diameter of the surviving route graph could be one of the fault-tolerance measures for the graph G and the routing p. When a routing is considered as a virtual path layout, we can discuss the fault tolerance of virtual path layouts in the ATM network. In this paper, we show that we construct three routings for any biconnected graph such that the diameter of the surviving route graphs is optimal and they satisfy some desirable properties of virtual path layouts in ATM networks.


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  1. 1.
    B.Bollobás: Extremal graph theory, Academic Press, 172(1978).Google Scholar
  2. 2.
    A.Broder, D.Dolev, M.Fischerand B.Simons: “Efficient fault tolerant routing in network,” Information and Computation75,52–64 (1987).Google Scholar
  3. 3.
    I.Cidon, O.Gerstel and S.Zaks: “A scalable approach to routing in ATM networks,” Proc. 8th International Workshop on Distributed Algorithms, LNCS 859, 209–222 (1994).Google Scholar
  4. 4.
    D.Dolev, J.Halpern, B.Simons and H.Strong: “A new look at fault tolerant routing,” Information and Computation72,180–196 (1987).Google Scholar
  5. 5.
    S. Evens: Graph algorithms, Computer Science Press, Potomac, Maryland(1979).Google Scholar
  6. 6.
    P.Feldman: “Fault tolerance of minimal path routing in a network,in Proc. 17th ACM STOC,pp,327–334(1985).Google Scholar
  7. 7.
    L.Gçasieniec, E.Kranakis, D. Krizanc and A.Pelc: “Minimizing Congestion of Layouts for ATM Networks with Faulty Links,” Proc. The 21st International Symposium on Mathematical Foundations of Computer Science, LNCS 1113, 372–381 (1996).Google Scholar
  8. 8.
    O.Gerstel, A. Wool and S.Zaks: “Optimal Layouts on a Chain ATM Network,” Proc. The 3rd Annual European Symposium on Algorithms, LNCS 979, 508–522 (1995).Google Scholar
  9. 9.
    O.Gerstel and S.Zaks: “The Virtual Path Layout roblem in Fast Networks,” Proc. 13th ACM Symposium on Principles of Distributed Computing, 235–243 (1994).Google Scholar
  10. 10.
    F.Harary, Graph theory, Addison-Wesley, Reading, MA(1969).Google Scholar
  11. 11.
    A. ItaiO. and M. Rodeh: “The multi-tree approach to reliability in distributed networks,” Information and Computation 79,43–59 (1988).Google Scholar
  12. 12.
    K.Kawaguchi and K.Wada: “New results in graph routing,” Information and Computation, 106, 2, 203–233 (1993).Google Scholar
  13. 13.
    J.Y.Le Boudec: “The Asynchronous Transfer Mode:A Tutorial,” Computer Networks and ISDN Systems, 24, 279–309 (1992).Google Scholar
  14. 14.
    H.Nagamochi and T.Ibaraki: “A linear-time algorithm for finding a sparse kconnected spanning subgraph of a k-connected graph,” Algorithmica, 7, 5/6, 583–596 (1992).Google Scholar
  15. 15.
    D.Peleg and B.Simons: “On fault tolerant routing in general graph,” Information and Computation74,33–49 (1987).Google Scholar
  16. 16.
    H.Suzuki, N.Takahashi and T.Nishizeki: “A linear algorithm for bipartition of biconnected graphs,” Information Processing Letters, 33, 5, 227–231 (1990).Google Scholar
  17. 17.
    K.Wada and K.Kawaguchi: “Efficient fault-tolerant fixed routings on (k + 1)connected digraphs,” Discrete Applied Mathematics, 37/38, 539–552 (1992).Google Scholar
  18. 18.
    K.Wada, Y.Luo and K.Kawaguchi: “Optimal Fault-tolerant routings for Connected Graphs,” Information Processing Letters, 41, 3, 169–174 (1992).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Koichi Wada
    • 1
  • Wei Chen
    • 1
  • Yupin Luo
    • 2
  • Kimio Kawaguchi
    • 3
  1. 1.Nagoya Institute of TechnologyNagoya
  2. 2.Department of AutomationTsinghua UniversityBeijingP.R.China
  3. 3.Osaka Institute of TechnologyHirakataJapan

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