2 at the MPLS layer. As a matter of fact, more hops generally means longer transmission and more costly DWDM. Let us assume that H is the maximum number of elements different from zero in one slice of [sR] obtained by ijkdv varying k and d and maintaining constant the other indices. Let us also assume that it is the same for all the layers. Due to the meaning of the elements of [sR], H results to be the maximum number of hops of a GLSP on layer S. The matrixes [sR] have a maximum number of SN2H2 elements different from zero, which in the previous example is 900 for S = 1 and 400 for S = 2. Moreover, as we will see in detail, the property that all GLSP are bidirectional can be used to further reduce the number of variables, arriving to 450 for S = 1 and 200 for S = 2 out of a total of 30,000. Thus, if it is needed to compact the representation of the matrixes [sR], it is possible to adopt a sparse matrix representation. This can be also beneficial to speed up searches in the matrix and thus calculation. One way to do that is to represent [sR] through a 2N X 2N X M pointers matrix and to append to each pointer a list of the only nonzero elements with the first two and the last indexes equal to the indexes of the pointer. The records of the list will be H2 and each of them will contain the third and the fourth indexes of the nonzero element of [sR]. This representation has also an important physical meaning that helps in implementing the algorithm. The first two indices are the two ends of an LSP while the last index is the Convergent Network Management and Control Plane order number of that LSP among all those with the same ends. Thus every pointer repre- sents an LSP and it points to records representing the links traversed at layer S by that LSP. The computation complexity of the final algorithm is a different issue, which is also trig- gered by the great number of design variables and we will discuss it at the end of the section. Returning to the definition of the routing matrixes, it is relevant to underline th