Combinatorial constructions of fault-tolerant routings with levelled minimum optical indices

Authors:
Xiande Zhang;Gennian Ge
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 4
Cited 0

Efficient routing in optical networks

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Fault-tolerant routings with minimum optical index

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Abstract

The design of fault-tolerant routings with levelled minimum optical indices plays an important role in the context of optical networks. However, not much is known about the existence of optimal routings with levelled minimum optical indices besides the results established by Dinitz, Ling and Stinson via the partitionable Steiner quadruple systems approach. In this paper, we introduce a new concept of a large set of even levelled P"3@?-design of order v and index 2, denoted by (v,P"3@?,2)-LELD, which is equivalent to an optimal, levelled (v-2)-fault-tolerant routing with levelled minimum optical indices of the complete network with v nodes. On the basis of the theory of three-wise balanced designs and partitionable candelabra systems, several infinite classes of (v,P"3@?,2)-LELDs are constructed. As a consequence, the existence problem for optimal routings with levelled minimum optical indices is solved for nearly a third of the cases.