AF: Small: Algorithmic Problems in Applied Computational Geometry

计算机技术在现代医学和生命科学中发挥着重要作用，特别是在诊断成像、人类基因组研究、治疗优化和医学数据管理方面。生物医学领域中出现的许多计算问题需要高效和高质量的算法解决方案。这个项目旨在开发新的几何计算和算法技术来解决生物医学和工程应用中的计算问题。本研究研究了一些具有理论挑战性和实际意义的几何优化问题。目标问题属于计算几何的基本问题，如几何划分、覆盖、整形、逼近、运动规划、聚类等，也出现在放射治疗、医学成像、生物学、计算机辅助制造、数据挖掘等重要应用领域。在这项研究的初步研究期间开发的一些算法和软件为实际应用问题提供了明显更好的解决方案(例如，与当前商业放射治疗计划系统计算的计划相比，放射癌症治疗计划有了很大改善)。这项研究将从其他理论领域汲取不同的技术，如图形算法、组合优化、离散数学和运筹学。它还将提供丰富的有趣的新问题/问题和新想法的来源，以促进计算几何和其他理论领域算法技术的进一步发展。该项目预计将产生更广泛的影响，超越计算几何，甚至计算机科学。它将产生高效有效的算法和软件，用于解决放射癌症治疗和外科、医学成像、生物学等应用领域的关键问题。此外，新开发的算法和软件将被纳入临床放射癌症治疗系统等实际应用中。因此，这项研究将有助于统一和整合计算几何、计算机算法和现代生物医学在诊断成像、放射癌症治疗等方面的应用，提高患者的生活质量。

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.