Abstract
The construction of light-trees is one principal subproblem for multicast routing in sparse splitting Wavelength Division Multiplexing (WDM) networks. Due to the light splitting constraint and the absence of wavelength converters, several light-trees may be required to establish a multicast session. However, the computation of optimal multicast light-trees is NP-hard. In this paper, we study the wavelength channel cost (i.e., total cost) of the light-trees built for a multicast session. An equal cost of 1 unit hop-count cost is assumed over all the fiber links in the network. We prove that the total cost of a multicast session is tightly lower limited to K and upper bounded to (1) K(N − K) when \(K<\frac{N}{2}\); (2) \(\frac{N^2-1}{4}\) or \(\frac{N^2}{4}\) respectively when \(K \geq \frac{N}{2}\) and N is odd or even, where K is the number of destinations in the multicast session and N is the number of nodes in the network. Classical sparse splitting multicast routing algorithms such as Reroute-to-Source and Member-Only [3] also follow these bounds. And particularly in WDM rings, the optimal multicast light-tree has a cost inferior to \(N-\lceil \frac{N}{K+1} \rceil\).
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Zhou, F., Molnár, M., Cousin, B., Qiao, C. (2010). Cost Bounds of Multicast Light-Trees in WDM Networks. In: Crovella, M., Feeney, L.M., Rubenstein, D., Raghavan, S.V. (eds) NETWORKING 2010. NETWORKING 2010. Lecture Notes in Computer Science, vol 6091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12963-6_27
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DOI: https://doi.org/10.1007/978-3-642-12963-6_27
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