A two-phase algorithm for the star-star concentrator location problem

The introduction of concentrators in a centralized telecommunication network is considered. The Star-Star (SS) network model is described, and the Star-Star concentrator location problem (SSCLP) is examined. The SSCLP is NP-complete and can be formulated as a 0-1 integer programming problem. A two-phase algorithm is developed to solve the SSCLP. In the first phase, dualizing the side constraints produces a Lagrangian problem that is easy to solve and whose optimal value is a lower bound (for minimization problems) on the optimal value of the original SSCLP. Then, heuristics are applied to produce an upper bound (feasible solution) to the SSCLP. In the second phase, branch-and-bound is used to refine the solution space to obtain a tighter lower bound. Computational examples with up to 100 terminals and 30 potential concentrators are considered. All the network designs obtained are shown to be within 2% of optimal.<>