Résumé
Multicast routing applied to optical networks provide several research problems on spanning tree. In optical networks, the ability of dividing the light signal is limited. Two recently problems try to take into account this constraint: looking for spanning trees with minimum number of branching vertices (vertices of degree strictly greater than 2) and looking for spanning trees such that the sum of branch vertices degrees is minimal. There are two kinds of optical nodes: nodes equipped with splitters, able to divide the input light signal, and nodes without splitters, unable to split the signal. The two problems mentioned above do not distinguish between the type of nodes. In this study, we discuss the relationship between the two problems, we thus prove that the two previous problems are not necessarily linked. We also propose two variants of them, taking into account this additional constraint in the construction of the spanning tree, and we find an experimental upper bound on the number of nodes to equip with splitters in an optical network.