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Designing Hypergraph Layouts to GMPLS Routing Strategies

  • Jean-Claude Bermond
  • David Coudert
  • Joanna Moulierac
  • Stéphane Pérennes
  • Ignasi Sau
  • Fernando Solano Donado
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)

Abstract

All-Optical Label Switching (AOLS) is a new technology that performs packet forwarding without any Optical-Electrical-Optical (OEO) conversions. In this paper, we study the problem of routing a set of requests in AOLS networks using GMPLS technology, with the aim of minimizing the number of labels required to ensure the forwarding. We first formalize the problem by associating to each routing strategy a logical hypergraph whose hyperarcs are dipaths of the physical graph, called tunnels in GMPLS terminology. Such a hypergraph is called a hypergraph layout, to which we assign a cost function given by its physical length plus the total number of hops traveled by the traffic. Minimizing the cost of the design of an AOLS network can then be expressed as finding a minimum cost hypergraph layout.

We prove hardness results for the problem, namely for general directed networks we prove that it is NP-hard to find a C logn-approximation, where C is a a positive constant and n is the number of nodes of the network. For symmetric directed networks, we prove that the problem is APX-hard. These hardness results hold even is the traffic instance is a partial broadcast. On the other hand, we provide an \(\mathcal{O}(\log n)\)-approximation algorithm to the problem for a general symmetric network. Finally, we focus on the case where the physical network is a path, providing a polynomial-time dynamic programming algorithm for a bounded number of sources, thus extending the algorithm given in [1] for a single source.

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References

  1. 1.
    Bermond, J.-C., Coudert, D., Moulierac, J., Perennes, S., Rivano, H., Sau, I., Solano Donado, F.: MPLS label stacking on the line network. In: Fratta, L., Schulzrinne, H., Takahashi, Y., Spaniol, O. (eds.) NETWORKING 2009. LNCS, vol. 5550, pp. 809–820. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Bermond, J.-C., Marlin, N., Peleg, D., Pérennes, S.: Directed virtual path layouts in ATM networks. Theoretical Computer Science 291(1), 3–28 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bern, M., Plassmann, P.: The Steiner problem with edge lengths 1 and 2. Information Processing Letters 32, 171–176 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bhatnagar, S., Ganguly, S., Nath, B.: Creating Multipoint-to-Point LSPs for traffic engineering. IEEE Commun. Mag. 43(1), 95–100 (2005)CrossRefGoogle Scholar
  5. 5.
    Charikar, M., Chekuri, C., Cheung, T., Dai, Z., Goel, A., Guha, S., Li, M.: Approximation algorithms for directed Steiner problems. In: Proc. of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 192–200 (1998)Google Scholar
  6. 6.
    Gerstel, O., Wool, A., Zaks, S.: Optimal layouts on a chain ATM network. Discrete Applied Mathematics 83, 157–178 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Goemans, M.X., Goldberg, A.V., Plotkin, S., Shmoys, D.B., Tardos, E., Williamson, D.P.: Improved approximation algorithms for network design problems. In: Proc. of the 5th annual ACM-SIAM symposium on Discrete algorithms (SODA), pp. 223–232 (1994)Google Scholar
  8. 8.
    Khuller, S., Vishkin, U.: Biconnectivity approximations and graph carvings. Journal of the ACM 41, 214–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ramos, F., et al.: IST-LASAGNE: Towards all-optical label swapping employing optical logic gates and optical flip-flops. IEEE J. Sel. Areas Commun. 23(10), 2993–3011 (2005)Google Scholar
  10. 10.
    Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proc. of the 29th annual ACM Symposium on Theory of Computing (STOC), pp. 475–484 (1997)Google Scholar
  11. 11.
    Saito, H., Miyao, Y., Yoshida, M.: Traffic engineering using multiple MultiPoint-to-Point LSPs. In: Proc. of IEEE INFOCOM, pp. 894–901 (2000)Google Scholar
  12. 12.
    Solano, F., Caenegem, R.V., Colle, D., Marzo, J.L., Pickavet, M., Fabregat, R., Demeester, P.: All-optical label stacking: Easing the trade-offs between routing and architecture cost in all-optical packet switching. In: Proc. of IEEE INFOCOM, pp. 655–663 (2008)Google Scholar
  13. 13.
    Solano, F., Fabregat, R., Marzo, J.: On optimal computation of MPLS label binding for MultiPoint-to-Point connections. IEEE Trans. Commun. 56(7), 1056–1059 (2007)CrossRefGoogle Scholar
  14. 14.
    Solano, F., Moulierac, J.: Routing in All-Optical Label Switched-based Networks with Small Label Spaces. In: Proc. of the 13th Conference on Optical Network Design and Modeling, ONDM (2009)Google Scholar
  15. 15.
    Solano, F., Stidsen, T., Fabregat, R., Marzo, J.: Label space reduction in MPLS networks: How much can one label do? IEEE/ACM Trans. Netw. (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-Claude Bermond
    • 1
  • David Coudert
    • 1
  • Joanna Moulierac
    • 1
  • Stéphane Pérennes
    • 1
  • Ignasi Sau
    • 1
    • 2
  • Fernando Solano Donado
    • 3
  1. 1.Mascotte joint project , I3S(CNRS-UNS) INRIASophia-AntipolisFrance
  2. 2.Applied Mathematics IV Department of UPCBarcelonaSpain
  3. 3.Institute of TelecommunicationsWarsaw University of TechnologyPoland

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