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In this paper, we investigate the Frequency Domain Packet Scheduling (FDPS) problem for 3GPP Long Term Evolution (LTE) Uplink (UL). Instead of studying a specific scheduling policy, we provide a unified approach to tackle this issue. First, we formalize a general LTE UL FDPS problem, which is suitable for various scheduling policies. Then, we prove that the problem is MAX SNP-hard, which implies that approximation algorithms with constant approximation ratios are the best that we can hope for. Therefore, we design two approximation algorithms, both of which have polynomial runtime. The first algorithm is based on a simple greedy method. The second one is based on the Local Ratio (L-R) technique and it can approximately solve the LTE UL FDPS problem with an approximation ratio of 2. To further analyze the stability of the 2-approximation L-R algorithm, we derive a specific FDPS problem, which incorporates the queue length and channel quality information. We utilize the Lyapunov Drift to prove the L-R algorithm is stable for any (ω0,ϵ0)-admissible LTE UL systems. The simulation results indicate good performance of the L-R scheduler.