Approximating the traffic grooming problem

The problem of grooming is central in studies of optical networks. In graph-theoretic terms, this can be viewed as assigning colors to the lightpaths so that at most g of them (g being the grooming factor) can share one edge. The cost of a coloring is the number of optical switches (ADMs); each lightpath uses two ADMs, one at each endpoint, and in case g   lightpaths of the same wavelength enter through the same edge to one node, they can all use the same ADM (thus saving g−1g−1 ADMs). The goal is to minimize the total number of ADMs. This problem was shown to be NP-complete for g=1g=1 and for a general g  . Exact solutions are known for some specific cases, and approximation algorithms for certain topologies exist for g=1g=1. We present an approximation algorithm for this problem. For every value of g   the running time of the algorithm is polynomial in the input size, and its approximation ratio for a wide variety of network topologies—including the ring topology—is shown to be 2lng+o(lng)2lng+o(lng). This is the first approximation algorithm for the grooming problem with a general grooming factor g.