  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 $C' \in \{1,2,3\}$. 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 $K_n$ 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.
