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 cc 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 nn-vertex mm-edge graph is determined here for all nn, mm, and c∈{2,3,4}c∈{2,3,4}. Indeed it is shown that in these cases drop cost and load can be minimized simultaneously.