We study grooming for two-period optical networks, a variation of the traffic
grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and
Syrotiuk. In the two-period grooming problem, during the first period of time,
there is all-to-all uniform traffic among n nodes, each request using 1/C
of the bandwidth; and during the second period, there is all-to-all uniform
traffic only among a subset V of v nodes, each request now being allowed to
use 1/C′ of the bandwidth, where C′<C. We determine the minimum drop cost
(minimum number of ADMs) for any n,v and C=4 and C′∈{1,2,3}. To do
this, we use tools of graph decompositions. Indeed the two-period grooming
problem corresponds to minimizing the total number of vertices in a partition
of the edges of the complete graph Kn into subgraphs, where each subgraph
has at most C edges and where furthermore it contains at most C′ edges of
the complete graph on v specified vertices. Subject to the condition that the
two-period grooming has the least drop cost, the minimum number of wavelengths
required is also determined in each case