Flow Trees : a Lower Bound Computation Tool forNetwork

This paper presents a new method for computing the lower bounds for multihop network design problems which is particularly well suited to optical networks. More speciically, given N stations each with d transceivers and pairwise average traac values of the stations, the method provides a lower bound for the combined problem of nding optimum (i) allocation of wavelengths to the stations to determine a connguration, and (ii) routing of the traac on this connguration while minimizing congestion-deened as the maximum ow assigned on any link. The lower bounds can be computed in time polynomial in the network size. Consequently, the results in this work yield a tool which can be used in (i) evaluating the quality of heuristic design algorithms, and (ii) determining a termination criteria during minimization. The lower bound computation is based on rst building ow trees to nd a lower bound on the total ow, and then distributing the total ow over the links to minimize the congestion.