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Extra resources for Applications of resource optimization in wireless networks
34) (i,j)∈A We use two sets of variables in the formulation of the subproblem. sij = vi = 1 if link (i, j) is included in the transmission group, 0 otherwise, 1 0 if node i is transmitting, otherwise. 34), can be stated as follows. 39) vi = 0/1, ∀i ∈ N. 34) is non-negative. 3 Enhancements The performance of the column generation method depends on the computing eﬀort of one iteration (in particular for solving the subproblem), as well as the total number of iterations before reaching optimality.
We ﬁrst present two linear integer formulations: a node-slot formulation for MNP, and a link-slot formulation for MLP. We then formulate the two problems using set covering formulations, for which we will derive the column generation method. , |T |} be a set of time slots. To ensure feasibility of MNP, it is suﬃcient to have |T | = |N |. We introduce the following binary variables. xit = yt = 1 0 1 0 if time slot t is assigned to node i otherwise. if time slot t is used otherwise. MNP can be formulated using the following node-slot formulation (NSF).
E. the set of transmission groups derived by TDMA). When the master problem is solved, we need to identify whether it can be improved by adding new columns (transmission groups) to L0N . In LP terms, this amounts to examining whether there exists any transmission group l ∈ LN , for which the corresponding variable xl has a strictly negative reduced cost. 23). 25) is negative. We are thus interested in the following optimization problem. β¯i sil . 26), but formulated differently. We use the following variables in the subproblem.