Abstract
AbstractWe study the minimization of ADMs (Add‐Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all‐to‐all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor C and N, the size of the ring. We first study exhaustively the cases C = 1, C = 2, and C = 3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case C > 3, focusing specifically on the case C = k(k + 1)/2 for some k ≥ 1. We give optimal decompositions for several congruence classes of N using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 58(1), 20–35 2011
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