Abstract
We consider the problem of minimizing the number of regenerators in optical networks with traffic grooming. In this problem we are given a network with an underlying topology of a graph G, a set of requests that correspond to paths in G and two positive integers g and d. There is a need to put a regenerator every d edges of every path, because of a degradation in the quality of the signal. Each regenerator can be shared by at most g paths, g being the grooming factor. On the one hand, we show that even in the case of d = 1 the problem is APX − hard, i.e. a polynomial time approximation scheme for it does not exist (unless P = NP). On the other hand, we solve such a problem for general G and any d and g, by providing an O(logg)-approximation algorithm and thus extending previous results holding only for specific topologies and specific values of d or g.
This work was partially supported by the Israel Science Foundation grant No. 1249/08, and by the PRIN 2008 research project COGENT (COmputational and GamE-theoretic aspects of uncoordinated NeTworks), funded by the Italian Ministry of University and Research.
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Flammini, M., Monaco, G., Moscardelli, L., Shalom, M., Zaks, S. (2011). On the Complexity of the Regenerator Cost Problem in General Networks with Traffic Grooming. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_8
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