AF: Small: Algorithmic Problems in Applied Computational Geometry

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Computer technologies play an important role in modern medicine and lifesciences, especially in diagnostic imaging, human genome study, treatmentoptimization, and medical data management. Many computational problems arising in the field of biomedicine call for efficient and good quality algorithmic solutions. This project aims to develop new geometric computing and algorithmic techniques for solving computational problems in biomedical and engineering applications.This research investigates a number of geometric optimization problems that are theoretically challenging and practically relevant. The target problems belong to fundamental topics of computational geometry, such as geometric partition, covering, shaping, approximation, motion planning, and clustering; they also arise in important applied areas such as radiation cancer treatment, medical imaging, biology, computer-aided manufacturing, and data mining. Some of the algorithms and software developed during the preliminary studies of this research have produced significantly better solutions for real application problems (for example, much improved radiation cancer therapy plans over those computed by thecurrent commercial radiation treatment planning systems). The research will draw diverse techniques from other theoretical areas such as graph algorithms, combinatorial optimization, discrete mathematics, and operations research. It will also provide a rich source of interesting new problems/questions and new ideas to prod further development of algorithmic techniques in computational geometry and other theoretical areas. This project is expected to generate broader impacts beyond computational geometry and even computer science. It will produce efficient and effective algorithms and software for solving key problems in radiation cancer therapy and surgery, medical imaging, biology, and other applied areas. Furthermore, the newly developed algorithms and software will be incorporated into practical applications such as clinical radiation cancer treatment systems. Hence, this research will help unite and integrate the power of computational geometry, computer algorithms, and modern biomedicine for diagnostic imaging, radiation cancer treatment, and other applications, and improve the quality of life for the patients.