Cost Bounds of Multicast Light-trees in WDM Networks

International audienceThe 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 < N/2 ; (2) (N^2 −1)/4 or (N^2)/4 respectively when K ≥ 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 multi- cast 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 − ⌈ N/( K+1) ⌉