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The study and design of Joint Radio Resource Management (JRRM) techniques is a key and challenging aspect in future heterogeneous wireless systems where different Radio Access Technologies (RAT) will physically coexist. In these systems, the total available radio resources need to be used in a coordinated way to guarantee adequate satisfaction levels to all users, and maximize the system revenues. In addition to carry out an efficient use of the available radio resources, JRRM algorithms need to exhibit good computational performance to guarantee their future implementation viability. In this context, this paper proposes novel JRRM techniques based on linear programming techniques, and investigates their computational cost when implemented in DSP platforms commonly used in mobile-based stations. The obtained results demonstrate the feasibility to implement the proposed JRRM algorithms in future heterogeneous wireless systems.