Cost Bounds and Approximation Ratios of Multicast Light-trees in WDM Networks

The construction of light-trees is one of the principal subproblems for all-optical 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 the cost-optimal multicast light-trees is NP-hard. In this paper, first we study the cost bounds of the light-trees built for a multicast session in unweighted WDM networks. Then, partially based on this result, the approximation ratios of some classical multicast light-tree computation algorithms, i.e., the reroute-to-source (R2S) and member-only (MO) algorithms, are derived in both unweighted and non-equally-weighted WDM networks. Moreover, integer linear programming formulations are introduced and carried out to search the optimal light-trees for multicast routing. The cost bounds and approximation ratios of the R2S and MO algorithms in some candidate WDM backbone networks are examined through simulations.