Grooming traffic to minimize load

Grooming traffic in optical networks can be formulated as partitioning the edges of a graph into subgraphs each having at most a specified number c of edges; a typical objective is to minimize the sum over all subgraphs of the vertices of nonzero degree (the drop cost). In practice, however, one may be constrained so that each vertex has nonzero degree in a limited number of different subgraphs of the partition. This is the load on the vertex, and the load of the grooming is the largest load at any vertex. The minimum load of a grooming for an n-vertex m-edge graph is determined here for all n, m, and c ∈ {2, 3, 4}. Indeed it is shown that in these cases drop cost and load can be minimized simultaneously. 1 Graph Decomposition and Grooming A unidirectional SONET ring connects n nodes in a circular fashion. Naming the nodes 0, . . . , n− 1, a connection is provided from node i to node i + 1 mod n for 0 ≤ i < n. Each connection supports a number of independent wavelengths on which communications can