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We study grooming for two-period optical networks, a variation of the trafficgrooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, andSyrotiuk. 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 uniformtraffic only among a subset $V$ of $v$ nodes, each request now being allowed touse $1/C'$ 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 dothis, we use tools of graph decompositions. Indeed the two-period groomingproblem corresponds to minimizing the total number of vertices in a partitionof the edges of the complete graph $K_n$ into subgraphs, where each subgraphhas at most $C$ edges and where furthermore it contains at most $C'$ edges ofthe complete graph on $v$ specified vertices. Subject to the condition that thetwo-period grooming has the least drop cost, the minimum number of wavelengthsrequired is also determined in each case.

Drop cost and wavelength optimal two-period grooming with ratio 4