Radiation therapy, treating over half of all cancer patients, involves using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient leads to solving large-scale constrained optimization problems that need to be solved within tight clinical time-frame. At the core of these challenges is a large matrix that is commonly sparsified for computational efficiency by neglecting small elements. Such a crude approximation can degrade the quality of treatment, potentially causing unnecessary radiation exposure to healthy tissues—this may lead to significant radiation-induced side effects—or delivering inadequate radiation to the tumor, which is crucial for effective tumor treatment. In this work, we demonstrate, for the first time, that randomized sketch tools can effectively sparsify this matrix without sacrificing treatment quality. We also develop a novel randomized sketch method with desirable theoretical guarantees that outperforms existing techniques in practical application. Beyond developing a novel randomized sketch method, this work emphasizes the potential of harnessing scientific computing tools, crucial in today's big data analysis, to tackle computationally intensive challenges in healthcare. The application of these tools could have a profound impact on the lives of numerous cancer patients. Code and sample data available at https://github.com/PortPy-Project/CompressRTP