On minimizing the number of ADMs in a general topology optical network Original Research Article

Minimizing the number of electronic switches in optical networks has been a main research topic in some recent studies. In such networks, we assign colors to a given set of lightpaths, and they are partitioned into unicolor cycles and paths; the switching cost is minimized when the number of paths is minimized. Most approximation and heuristic algorithms for this problem have a preprocessing stage, in which possible cycles are found. Among them, the basic algorithm eliminates cycles of size at most image, and has a performance guarantee of image, where image is the cost of an optimal solution, image is the number of lightpaths and image, for any given odd image. The time complexity of the algorithm is exponential in image. We improve the analysis of this algorithm, by showing that image, which implies a reduction of the exponent in the time complexity. We also improve the lower bound by showing that image. The results shed more light on the structure of this basic algorithm. In addition, in our analysis we suggest a novel technique–including a new combinatorial lemma–to deal with this problem.