  To minimize the number of wavelengths required by a multicast session in
sparse light splitting wavelength division multiplexing (WDM) networks, a
light-hierarchy structure, which occupies the same wavelength on all links, is
proposed to span as many destinations as possible. Different from a light-tree,
a light-hierarchy accepts cycles, which are used to traverse crosswise a
4-degree (or above) multicast incapable (MI) node twice (or above) and switch
two light signals on the same wavelengths to two destinations in the same
multicast session. In this paper, firstly, a graph renewal and distance
priority light-tree algorithm (GRDP-LT) is introduced to improve the quality of
light-trees built for a multicast request. Then, it is extended to compute
light-hierarchies. Obtained numerical results demonstrate the GRDP-LT
light-trees can achieve a much lower links stress, better wavelength channel
cost, and smaller average end-to-end delay as well as diameter than the
currently most efficient algorithm. Furthermore, compared to light-trees, the
performance in terms of link stress and network throughput is greatly improved
again by employing the light-hierarchy, while consuming the same amount of
wavelength channel cost.
