Approximating the traffic grooming problem in tree and star networks

Authors:
Michele Flammini;Gianpiero Monaco;Luca Moscardelli;Mordechai Shalom;Shmuel Zaks
Affiliations:
Dipartmento di Informatica, Universita degli Studi dell'Aquila, L'Aquila, Italy;Dipartmento di Informatica, Universita degli Studi dell'Aquila, L'Aquila, Italy;Dipartmento di Informatica, Universita degli Studi dell'Aquila, L'Aquila, Italy;Department of Computer Science, Technion, Haifa, Israel;Department of Computer Science, Technion, Haifa, Israel
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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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 (δg) + o(ln (δg)) 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.