Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or OOD detection (https://arxiv.org/abs/2603.23558). Within credal approaches that consider modeling uncertainty as probability sets, upper entropy plays a central role as an uncertainty measure. This paper is devoted to the computational aspect of upper entropies, providing an exhaustive algorithmic and complexity analysis of the problem (https://arxiv.org/abs/2603.23558). In particular, the researchers show that the problem has a strongly polynomial solution, and propose many significant improvements over past algorithms proposed for 2-monotone lower probabilities and their specific cases (https://arxiv.org/abs/2603.23558).