hat the variables have to be integer, substituting them with real variables. In the particular case in which there is a variable that can be zero or one, this is substituted with a real variable in between zero and one. The first case happens in our model, for example, for the number of wavelengths in a link and the second for the elements of the matrix [sR]. With these substitutions, the problem becomes a linear programming problem, whose complexity is polynomial, thus solvable also in high-dimensional cases. At the end, the optimum variables will not be integer in general, but the optimum of the LP problem will be a lower bound of the real problem solution; this lower bound is called LP-relaxation bound [20]. In order to derive an upper bound of the solution, the following algorithm can be used: Construct a problem-acceptable solution by rounding the LP optimum variables to the upper or lower integer as suited. Substitute these variables into the cost function to obtain the cost relative to the constructed network design. The obtained cost is an upper bound of the solution of the ILP problem. The first step of the algorithm is generally not unique and, if several possible networks can be designed rounding to integer value the LP solution, the tighter upper bound is rep- resented by the smaller cost corresponding to one of such networks. This upper bound is called rounding bound [20]. If the upper-bound and the lower bound are sufficiently near, the rounded variables constitute a good approximation of the effective ILP optimum solution. These simplifica- tion methods can make solvable a problem that is not solvable searching an exact solution, Convergent Network Management and Control Plane but the general nature of NP hard problem remains. This is why, in order to analyze large networks or to analyze a large number of alternatives, completely different design meth- ods have been introduced based on heuristic approaches. These methods provide subop- timum solutions, but are much less complex than ILP optimizatio