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Cycle Covering

Jean-Claude Bermond 1 Lilian Chacon 2 David Coudert 1 Francois Tillerot 2
1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : This paper considers the design of a survivable WDM network based on covering the initial network with sub-networks, which are protected independently from each other. We focus on the case where the optical WDM network is a ring, there are requests between any pair of vertices and the covering is done with small cycles. This problem can be modelled as follows: Find a covering of the edges of a logical graph I (here the complete graph Kn ) by subgraphs Ik of a certain kind (here cycles Ck of length k), such that, for each Ik , there exists in the physical graph G (here Cn ) a disjoint routing of the edges of Ik . The aim is to minimize the number of subgraphs Ik in the covering. We give optimal solutions for that problem.
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https://hal.inria.fr/inria-00429183
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Jean-Claude Bermond, Lilian Chacon, David Coudert, Francois Tillerot. Cycle Covering. 8th International Colloquium on Structural Information and Communication Complexity (SIROCCO), Jun 2001, Vall de Nuria, Spain. pp.21-34. ⟨inria-00429183⟩

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