In this paper, an optimal centralized approach to topology control (TC) is adopted where the network topology is established considering interference, k-connectivity and routing constraints. This optimization problem however involves link scheduling and power assignment under SINR constraint, which is an NP hard problem even for a small number of nodes. An exact solution beyond six nodes has not been found so far. Opting for heuristics rather than exact approach, the proposed algorithms in the literature, either cannot guarantee the quality of the solution, or approximate the interference (protocol interference model) rather than using realistic SINR models. Here, at first we present a novel formulation for the optimal solution and analyse its limits. We then propose a novel approximation algorithm using column generation (CG) together with knapsack transformation on the SINR constraint. Particle Swarm Optimization (PSO) is integrated into the CG, to provide robust initial feasible patterns. The results show that, CG-PSO with knapsack transformation increase the solvable instances three fold in terms of number of nodes, in comparison to the state-of-art approaches. The links are scheduled with less power and shorter scheduling lengths,while the proposed algorithm also reduces the computation time at lower penalty cost.
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