The Splitter Placement Problem: The Static Case

Abstract

We saw in the previous chapter that, realistically, only a subset of the cross-connects will be equipped with multicasting capabilities. Motivated by this observation, we introduce in this chapter the splitter placement in wavelength-routed networks (SP-WRN) problem. The SP-WRN problem is NP-complete as it includes as a subproblem the routing and wavelength assignment problem which is NP-complete. To gain a deeper insight into the computational complexity of the SP-WRN problem, we define a graph-theoretic version of the splitter placement problem (SPG), and show that even SPG is NP-complete. We develop three heuristics for the SP-WRN problem with different degrees of trade-off between computation time and quality of solution. The first heuristic uses the CPLEX general solver to solve an Integer-Linear Program (ILP) of the problem. The second heuristic is based on a greedy approach and is called Most-Saturated Node First (MSNF). The third heuristic employs Simulated Annealing (SA) with route-coordination. Through numerical examples on a wide variety of network topologies we demonstrate that: 1) no more than 50% of the cross-connects need to be multicast-capable, 2) the proposed SA heuristic provides fast near-optimal solutions, and 3) it is not practical to use general solvers such as CPLEX for solving the SP-WRN problem.