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A fundamental and computationally challenging optimization task in wireless networks is to maximize the number of simultaneous transmissions, subject to signal-to-noise-and-interference ratio (SINR) requirements at the receivers. The conventional approach guaranteeing global optimality is to solve an integer programming model with explicit SINR constraints. These constraints are however numerically very difficult. We develop a new integer programming algorithm based on a much more effective representation of the SINR constraints. Computational experiments demonstrate that the new approach performs significantly better in proving optimality.