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Approximating the Traffic Grooming Problem

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

The problem of grooming is central in studies of optical networks. In graph-theoretic terms, this can be viewed as assigning colors to the lightpaths so that at most g of them (g being the grooming factor) can share one edge. The cost of a coloring is the number of optical switches (ADMs); each lightpath uses two ADM’s, one at each endpoint, and in case g lightpaths of the same wavelength enter through the same edge to one node, they can all use the same ADM (thus saving g – 1 ADMs). The goal is to minimize the total number of ADMs. This problem was shown to be NP-complete for g = 1 and for a general g. Exact solutions are known for some specific cases, and approximation algorithms for certain topologies exist for g = 1. We present an approximation algorithm for this problem. For every value of g the running time of the algorithm is polynomial in the input size, and its approximation ratio for a wide variety of network topologies – including the ring topology – is shown to be 2 ln g + o(ln g). This is the first approximation algorithm for the grooming problem with a general grooming factor g.

This research was supported in part by the EU COST 293 (GRAAL) research fund.

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© 2005 Springer-Verlag Berlin Heidelberg

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Flammini, M., Moscardelli, L., Shalom, M., Zaks, S. (2005). Approximating the Traffic Grooming Problem. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_91

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  • DOI: https://doi.org/10.1007/11602613_91

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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