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The HTTP adaptive streaming technique opened the door to cope with the fluctuating network conditions during the streaming process by dynamically adjusting the volume of the future chunks to be downloaded. The bitrate selection in this adjustment inevitably involves the task of predicting the future throughput of a video session, owing to which various heuristic solutions have been explored. The ultimate goal of the present work is to explore the theoretical upper bounds of the QoE that any ABR algorithm can possibly reach, therefore providing an essential step to benchmarking the performance evaluation of ABR algorithms. In our setting, the QoE is defined in terms of a linear combination of the average perceptual quality and the buffering ratio. The optimization problem is proven to be NP-hard when the perceptual quality is defined by chunk size and conditions are given under which the problem becomes polynomially solvable. Enriched by a global lower bound, a pseudo-polynomial time algorithm along the dynamic programming approach is presented. When the minimum buffering is given higher priority over higher perceptual quality, the problem is shown to be also NP-hard, and the above algorithm is simplified and enhanced by a sequence of lower bounds on the completion time of chunk downloading, which, according to our experiment, brings a 36.0% performance improvement in terms of computation time. To handle large amounts of data more efficiently, a polynomial-time algorithm is also introduced to approximate the optimal values when minimum buffering is prioritized. Besides its performance guarantee, this algorithm is shown to reach 99.938% close to the optimal results, while taking only 0.024% of the computation time compared to the exact algorithm in dynamic programming.