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Preplanned Recovery Schemes Using Multiple Redundant Trees in Complete Graphs

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Future Control and Automation

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 173))

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Abstract

Zehavi and Itai have suggested a conjecture that implies we can use k disjoint trees to achieve up to k-1 simultaneous edge failures restoration for k-edge connected graphs or up to k-1 simultaneous node failures restoration for k-node connected graphs. In this paper, we firstly point out that a complete graph with n nodes is both (n-1)-edge connected and (n-1)-node connected. This implies that, provided that Zehavi’s conjecture is right, we can use n-1 disjoint trees for restoration. Although we have not demonstrated the correctness of Zehavi’s conjecture, we indeed construct two types of recovery schemes using multiple redundant trees for complete graphs, Hamilton-based recovery scheme and star-based recovery scheme, based on two types of decomposition of complete graphs. In complete graphs with n nodes, the latter can recover from any up to n-2 simultaneous link or node failures, and the former can recover from any up to n-2 simultaneous link or node failures if n is odd and any up to n-3 failures if n is even.

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References

  1. Alspach, B., Bermond, J.C., Sotteau: Decompositions into cycles I: Hamilton decompositions, cycles and rays, pp. 9–18. Kluwer Academic Press (1990)

    Google Scholar 

  2. Alspach, B., Gavlas, H.: Cycle decompositioins of Kn and Kn-I. J. Combin. Theory, Ser. B 81, 77–99 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Anand, V., Qiao, C.: Dynamic establishment of protection paths in WDM networks, part I. In: IEEE ICCCN 2000, pp. 198–204 (2000)

    Google Scholar 

  4. Choi, H., Subramaniam, S., Choi, H.-A.: On double-link failure recovery in WDM optical networks. In: IEEE Infocom 2002, pp. 808–816 (2002)

    Google Scholar 

  5. Choi, H., Subramaniam, S., Choi, H.-A.: Loopback recovery from double-link failures in optical mesh networks. IEEE/ACM Transactions on Networking 12, 1119–1130 (2004)

    Article  Google Scholar 

  6. Ellinas, G., Hailemariam, A.G., Stern, T.E.: Protection cycles in mesh WDM networks. IEEE Journal on Selected Areas in Communications 18, 1924–1937 (2000)

    Article  Google Scholar 

  7. Gross, J.L., Yellen, J.: Handbook of Graph theory. CRC Press (2004)

    Google Scholar 

  8. Grover, W.D., Stamatelakis, D.: Cycle-oriented distributed preconfigur-ation: ring-like speed with mesh-like capacity for self-planning network restoration. In: IEEE ICC 1988, pp. 537–543 (1998)

    Google Scholar 

  9. Guo, L., Wang, X.W., Du, J., Wu, T.F.: A new heuristic routing algorithm with Hamiltonian Cycle Protection in survivable networks. Computer Communications 31, 1672–1678 (2008)

    Article  Google Scholar 

  10. Guo, L., Wang, X.W., Wei, X.T., Yang, T., Hou, W.G., Wu, T.F.: A New Link-Based Hamiltonian Cycle Protection in Survivable WDM Optical Networks. In: AICT 2008, pp. 227–231 (2008)

    Google Scholar 

  11. Itai, A., Rodeh, M.: The multi-tree approach to reliablity in distributed networks. Information and Computation 79, 43–59 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jukan, A., Monitzer, A., de Marchis, G., Sabella, R. (eds.): Restoration methods for multi-service optical networks. Optical Networks: Design and Modelling, pp. 3–12. Kluwer Academic Publishers (1999)

    Google Scholar 

  13. Médard, M., Barry, R.A., Finn, S.G., He, W., Lumetta, S.S.: Generalized loop-back recovery in optical mesh networks. IEEE/ACM Trans. Net. 10, 153–164 (2002)

    Article  Google Scholar 

  14. Médard, M., Finn, S.G., Barry, R.A.: A novel approach to automatic protection switching using trees. In: IEEE ICC 1997, pp. 272–276 (1997)

    Google Scholar 

  15. Médard, M., Finn, S.G., Barry, R.A., Gallager, R.G.: Redundant trees for preplanned recovery in arbitrary vertex-redundant or edge-redundant graphs. IEEE/ACM Trans. Net. 7, 641–652 (1999)

    Article  Google Scholar 

  16. Mohan, G., Ram Murthy, C.S., Somani, A.K.: Efficient algorithms for routing dependable connections in WDM optical networks. IEEE/ACM Trans. Net. 9, 553–566 (2001)

    Article  Google Scholar 

  17. Mukherjee: WDM optical networks: progress and challenges. IEEE Journal on Selected Areas in Communications 18, 1810–1824 (2000)

    Article  Google Scholar 

  18. Mukherjee: Optical Communication Networks. McGraw Hill (1997)

    Google Scholar 

  19. Ouveysi, I., Wirth, A.: On design of a survivable network architecture for dynamic routing: optimal solution strategy and an efficient heuristic. European Journal of Operational Reshearch 117, 30–44 (1999)

    Article  MATH  Google Scholar 

  20. Ouveysi, I., Wirth, A.: Wirth, Minimal complexity heuristics for robust network architecture for dynamic routing. Journal of the Operational Research Society 50, 262–267 (1999)

    MATH  Google Scholar 

  21. Qiao, D.X.: Distributed partial information management (DPIM) schemes for survivable networks, part I. In: IEEE Infocom 2002, pp. 302–311 (2002)

    Google Scholar 

  22. Ramamurthy, S., Mukherjee, B.: Survivable WDM mesh networks, part I-protection. In: IEEE Infocom 1999, pp. 744–751 (1999)

    Google Scholar 

  23. Ramamurthy, S., Mukherjee, B.: Survivable WDM mesh networks, part II-restoration. In: IEEE ICC 1999, pp. 2023–2030 (1999)

    Google Scholar 

  24. Sahasrabuddhe, L., Ramamurthy, S., Mukherjee, B.: Fault management in IP-over-WDM networks: WDM protection versus IP restoration. IEEE Journal on Selected Areas in Communications 20, 21–33 (2002)

    Article  Google Scholar 

  25. Wu, T.H., Way, W.I.: A novel passive protected SONET bidirectional self-healing ring architecture. IEEE Journal of Lightwave Technology 10, 1314–1322 (1992)

    Article  Google Scholar 

  26. Xue, G., Chen, L., Thulasiraman, K.: QoS issues in redundant trees for protection in vertex-redundant or edge-redundant graphs. In: IEEE ICC 2002, pp. 2766–2770 (2002)

    Google Scholar 

  27. Xue, G., Chen, L., Thulasiraman, K.: Quality of service and quality protection issues in preplanned recovery schemes using redundant trees. IEEE Journal on Selected Areas in Communications; Optical Communications and Networking series 21, 1332–1345 (2003)

    Google Scholar 

  28. Zehavi, A.I.: Three tree-paths. J. Graph Theory 13, 175–188 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhang, W.Y., Xue, G., Tang, J., Thulasiraman, K.: Faster algorithms for constructing recovery trees enhancing QoP and QoS. IEEE/ACM Trans. Net. 16, 642–655 (2008)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Basic Education, Zhejiang Water Conservancy and Hydropower College, Hangzhou, Zhejiang Province, 310000, China

    Wei Ding

  2. Department of Computing Science, University of Alberta, Edmonton, Alberta, T6G 2E8, Canada

    Yi Shi

Authors
  1. Wei Ding
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  2. Yi Shi
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Correspondence to Wei Ding .

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Editors and Affiliations

  1. Nanhai Ave 3688, Shenzen, 518060, China, People's Republic

    Wei Deng

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Ding, W., Shi, Y. (2012). Preplanned Recovery Schemes Using Multiple Redundant Trees in Complete Graphs. In: Deng, W. (eds) Future Control and Automation. Lecture Notes in Electrical Engineering, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31003-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-31003-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31002-7

  • Online ISBN: 978-3-642-31003-4

  • eBook Packages: EngineeringEngineering (R0)

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