Résumé
The problem of grooming is central in studies of optical networks. In graph-theoretic terms, it can be viewed as assigning colors to given paths in a graph, so that at most g (the grooming factor) paths of the same color can share an edge. Each path uses an ADM at each of its endpoints, and paths of the same color can share an ADM in a common endpoint. There are two sub-models, depending on whether or not paths that have the same color can use more than two edges incident with the same node (bifurcation allowed and bifurcation not allowed, resp.). The goal is to find a coloring that minimizes the total number of ADMs. In a previous work it was shown that the problem is NP-complete when bifurcation is allowed, even for a star network. In tins paper we study the problem for a star network when bifurcation is not allowed. For the case of simple requests - in which only the case of g = 2 is of interest - we present a polynomial-time algorithm, and we study the structure of optimal solutions. We also present results for the case of multiple requests and g = 2, though the exact complexity of this case remains open. We provide two techniques, which lead to 4/3-approximation algorithms. Our algorithms reduce the problem of traffic grooming in star networks to several variants of maximum matching problems.