Grooming for Two-Period Optical Networks Charles J. Colbourn Computer Science and Engineering Arizona State University Tempe, AZ, 85287-8809, U.S.A. colbourn@asu.edu Gaetano Quattrocchi Dipartimento di Matematica e Informatica Universit`a di Catania viale A. Doria, 6 95125 Catania, Italy quattrocchi@dmi.unict.it Violet R. Syrotiuk Computer Science and Engineering Arizona State University Tempe, AZ, 85287-8809, U.S.A. syrotiuk@asu.edu Abstract Minimizing the number of add-drop multiplexers (ADMs) in a unidirectional SONET ring can be formulated as a graph decomposition problem. When traffic requirements are uniform and all-to-all, groomings that minimize the number of ADMs (equivalently, the drop cost) have been characterized for grooming ratio at most six. However, when two different traffic requirements are supported, these solutions do not ensure opti- mality. In two-period optical networks, n vertices are required to support a grooming ratio of C in the first time period, while in the second time period a grooming ratio of C ′ , C ′ <C , is required for v ≤ n vertices. This allows the two-period grooming problem to be expressed as an optimization problem on graph decompositions of K n that embed graph decompositions of K v for v ≤ n. Using this formulation, optimal two-period groomings are found for small grooming ratios using techniques from the theory of graphs and designs. Keywords: optical networks, traffic grooming, graph decomposition, combinatorial designs 1