CAREER: Algorithmic issues in geometric network optimization, binary space partitions, and metamorphic systems

职业：几何网络优化、二元空间划分和变质系统中的算法问题

• 批准号: 0444188
• 负责人: Adrian Dumitrescu
• 金额: $ 47.49万
• 依托单位: University of Wisconsin-Milwaukee
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0444188&HistoricalAwards=false
• 关键词: CAREER; Algorithmic; issues; geometric; network

The new variants of known problems (like traveling salesman, binary space partitions for space subdivisions, and geometric dilation) are being studied in order to produce new techniques and address key issues in algorithm design and approximation. Besides that, they are likely to have other implications. For example, the study of geometric dilation may provide better ways of designing transportation networks, and efficient ways for upgrading existing ones. The theoretical study of metamorphic systems is necessary for understanding their capabilities and for developing algorithms that control them. An important aspect of this research is advancing the integration of techniques from different areas --- discrete and combinatorial geometry, geometric graph theory, graph theory, topology, linear programming --- in the design of geometric algorithms. This research deals with algorithmic questions from the areas of computational geometry and robotics, grouped in three directions. The problems in the first category are in the area of geometric network optimization where the focus will be new variants of the classic traveling salesman problem that have emerged in the last decade, such as those with neighborhoods and the angle restricted tour problem. These efforts are aimed at understanding the differences between various classes of regions, which make some instances harder to approximate than others. A second research direction deals with cutting techniques applied to two important problems: binary space partitions and stock cutting algorithms. A third category includes fundamental questions generated by the study and analysis of metamorphic robotic systems, a relatively new research direction in robotics. Two basic capabilities of metamorphic systems are researched: reconfiguration and locomotion. Development of such systems is regarded as very promising, due to their versatility and high degree of fault tolerance. An important aspect of this research is advancing the integration of techniques from different areas --- discrete and combinatorial geometry, geometric graph theory, graph theory, topology, linear programming --- in the design of geometric algorithms.

已知问题的新变种（如旅行推销员，空间细分的二进制空间划分和几何膨胀）正在研究中，以产生新的技术和解决算法设计和近似的关键问题。除此之外，它们可能还有其他影响。例如，几何扩张的研究可以提供设计交通网络的更好方法，以及升级现有交通网络的有效方法。变形系统的理论研究对于理解它们的能力和开发控制它们的算法是必要的。该研究的一个重要方面是推进不同领域的技术-离散和组合几何，几何图论，图论，拓扑学，线性规划-在几何算法设计中的集成。 这项研究涉及计算几何和机器人领域的算法问题，分为三个方向。第一类中的问题是在几何网络优化领域，其中重点将是在过去十年中出现的经典旅行商问题的新变体，例如具有邻域的问题和角度受限的旅游问题。这些努力的目的是了解不同类别的区域之间的差异，这使得一些情况比其他情况更难近似。第二个研究方向涉及切割技术应用于两个重要的问题：二进制空间分区和股票切割算法。第三类包括变形机器人系统的研究和分析所产生的基本问题，这是机器人学中一个相对较新的研究方向。研究了变形系统的两个基本能力：重构和运动。这种系统的发展被认为是非常有前途的，由于其多功能性和高度的容错性。该研究的一个重要方面是推进不同领域的技术-离散和组合几何，几何图论，图论，拓扑学，线性规划-在几何算法设计中的集成。