Abstract
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
g) + o(ln (δ
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.
This research was partly supported by the EU Project “Graphs and Algorithms in Communication Networks (GRAAL)” – COST Action TIST 293.
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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)
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)
Bermond, J.-C., Coudert, D.: Traffic grooming in unidirectional WDM ring networks using design theory. In: IEEE ICC, Anchorage, Alaska (May 2003)
Brackett, C.A.: Dense wavelength division multiplexing networks: principles and applications. IEEE Journal on Selected Areas in Communications 8, 948–964 (1990)
Chen, B., Rouskas, G.N., Dutta, R.: Traffic grooming in star networks. In: Broadnets (2004)
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)
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)
Chung, N.K., Nosu, K., Winzer, G.: Special issue on dense wdm networks. IEEE Journal on Selected Areas in Communications 8 (1990)
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)
Călinescu, G., Wan, P.-J.: Traffic partition in wdm/sonet rings to minimize sonet adms. Journal of Combinatorial Optimization 6(4), 425–453 (2002)
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)
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)
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)
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)
Garey, M., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gargano, L., Vaccaro, U.: Routing in All–Optical Networks: Algorithmic and Graph–Theoretic Problems. In: Numbers, Information and Complexity. Kluwer Academic, Dordrecht (2000)
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)
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)
Green, P.E.: Fiber-Optic Communication Networks. Prentice-Hall, Englewood Cliffs (1992)
Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. System Sci. 9, 256–278 (1974)
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)
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)
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Flammini, M., Monaco, G., Moscardelli, L., Shalom, M., Zaks, S. (2006). Approximating the Traffic Grooming Problem in Tree and Star Networks. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_14
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DOI: https://doi.org/10.1007/11917496_14
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