Based on the false assumption that multicast incapable (MI) nodes could not
be traversed twice on the same wavelength, the light-tree structure was always
thought to be optimal for multicast routing in sparse splitting Wavelength
Division Multiplexing (WDM) networks. In fact, for establishing a multicast
session, an MI node could be crosswise visited more than once to switch a light
signal towards several destinations with only one wavelength through different
input and output pairs. This is called Cross Pair Switching (CPS). Thus, a new
multicast routing structure light-hierarchy is proposed for all-optical
multicast routing, which permits the cycles introduced by the CPS capability of
MI nodes. We proved that the optimal structure for minimizing the cost of
multicast routing is a set of light-hierarchies rather than the light-trees in
sparse splitting WDM networks. Integer linear programming (ILP) formulations
are developed to search the optimal light-hierarchies. Numerical results
verified that the light-hierarchy structure could save more cost than the
light-tree structure