Approximating the Traffic Grooming Problem in Tree and Star Networks

  • Michele Flammini
  • Gianpiero Monaco
  • Luca Moscardelli
  • Mordechai Shalom
  • Shmuel Zaks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)


We consider the problem of grooming paths in all-optical networks with tree topology so as to minimize the switching cost, measured by the total number of used ADMs. We first present efficient approximation algorithms with approximation factor of 2 ln (δ Open image in new window g) + o(ln (δ Open image in new window g)) for any fixed node degree bound δ and grooming factor g, and 2ln g+ o( ln g) in unbounded degree directed trees, respectively. In the attempt of extending our results to general undirected trees we completely characterize the complexity of the problem in star networks by providing polynomial time optimal algorithms for g ≤2 and proving the intractability of the problem for any fixed g >2. While for general topologies the problem was known to be NP-hard g not constant, the complexity for fixed values of g was still an open question.


Optical Networks Wavelength Division Multiplexing(WDM) Add-Drop Multiplexer(ADM) Traffic Grooming Tree Networks 


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  1. 1.
    Beauquier, B., Bermond, J.-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength–routing in all–optical networks. In: Proc. 2nd Workshop on Optics and Computer Science, WOCS 1997 (April 1997)Google Scholar
  2. 2.
    Bermond, J.-C., Braud, L., Coudert, D.: Traffic grooming on the path. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 34–48. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Bermond, J.-C., Coudert, D.: Traffic grooming in unidirectional WDM ring networks using design theory. In: IEEE ICC, Anchorage, Alaska (May 2003)Google Scholar
  4. 4.
    Brackett, C.A.: Dense wavelength division multiplexing networks: principles and applications. IEEE Journal on Selected Areas in Communications 8, 948–964 (1990)CrossRefGoogle Scholar
  5. 5.
    Chen, B., Rouskas, G.N., Dutta, R.: Traffic grooming in star networks. In: Broadnets (2004)Google Scholar
  6. 6.
    Chen, B., Rouskas, G.N., Dutta, R.: Traffic grooming in wdm ring networks with the min-max objective. In: Mitrou, N.M., Kontovasilis, K., Rouskas, G.N., Iliadis, I., Merakos, L. (eds.) NETWORKING 2004. LNCS, vol. 3042, pp. 174–185. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Chiu, A.L., Modiano, E.H.: Traffic grooming algorithms for reducing electronic multiplexing costs in wdm ring networks. Journal of Lightwave Technology 18(1), 2–12 (2000)CrossRefGoogle Scholar
  8. 8.
    Chung, N.K., Nosu, K., Winzer, G.: Special issue on dense wdm networks. IEEE Journal on Selected Areas in Communications 8 (1990)Google Scholar
  9. 9.
    Călinescu, G., Frieder, O., Wan, P.-J.: Minimizing electronic line terminals for automatic ring protection in general wdm optical networks. IEEE Journal of Selected Area on Communications 20(1), 183–189 (2002)CrossRefGoogle Scholar
  10. 10.
    Călinescu, G., Wan, P.-J.: Traffic partition in wdm/sonet rings to minimize sonet adms. Journal of Combinatorial Optimization 6(4), 425–453 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Du, D.H.C., Vetter, R.J.: Distributed computing with high-speed optical networks. In: Proceeding of IEEE Computer, vol. 26, pp. 8–18 (1993)Google Scholar
  12. 12.
    Eilam, T., Moran, S., Zaks, S.: Lightpath arrangement in survivable rings to minimize the switching cost. IEEE Journal of Selected Area on Communications 20(1), 172–182 (2002)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Epstein, L., Levin, A.: Better bounds for minimizing sonet adms. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 281–294. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Flammini, M., Moscardelli, L., Shalom, M., Zaks, S.: Approximating the traffic grooming problem. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 915–924. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Garey, M., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  16. 16.
    Gargano, L., Vaccaro, U.: Routing in All–Optical Networks: Algorithmic and Graph–Theoretic Problems. In: Numbers, Information and Complexity. Kluwer Academic, Dordrecht (2000)Google Scholar
  17. 17.
    Gerstel, O., Lin, P., Sasaki, G.: Wavelength assignment in a wdm ring to minimize cost of embedded sonet rings. In: INFOCOM 1998, Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies (1998)Google Scholar
  18. 18.
    Gerstel, O., Ramaswami, R., Sasaki, G.: Cost effective traffic grooming in wdm rings. In: INFOCOM 1998, Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies (1998)Google Scholar
  19. 19.
    Green, P.E.: Fiber-Optic Communication Networks. Prentice-Hall, Englewood Cliffs (1992)Google Scholar
  20. 20.
    Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. System Sci. 9, 256–278 (1974)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Klasing, R.: Methods and problems of wavelength-routing in all-optical networks. In: Proceeding of the MFCS 1998 Workshop on Communication, Brno, Czech Republic, August 24-25, pp. 1–9 (1998)Google Scholar
  22. 22.
    Shalom, M., Zaks, S.: A 10/7 + ε approximation scheme for minimizing the number of adms in sonet rings. In: First Annual International Conference on Broadband Networks, San-José, California, USA (October 2004)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michele Flammini
    • 1
  • Gianpiero Monaco
    • 1
  • Luca Moscardelli
    • 1
  • Mordechai Shalom
    • 2
  • Shmuel Zaks
    • 2
  1. 1.Dipartmento di InformaticaUniversita degli Studi dell’AquilaL’AquilaItaly
  2. 2.Department of Computer ScienceTechnionHaifaIsrael

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