AF: Small: Approximation Algorithms for Geometric Optimization

AF：小：几何优化的近似算法

• 批准号: 1018388
• 负责人: Joseph S. Mitchell
• 金额: $ 48.28万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018388&HistoricalAwards=false
• 关键词: AF; Small; Approximation; Algorithms; Geometric; AF; Small; Approximation; Algorithms; Geometric

The methodologies of computational geometry will be applied to design,analyze, implement, and test algorithms for problems that arise inseveral application areas, including geometric network optimization,air traffic management, sensor networks, robotics, geometric modeling,and manufacturing. The main project goal is the development offundamental advances in approximation algorithms for geometricproblems. Additionally, the project will strive to foster and deepencollaborations with researchers and domain experts in applicationareas and industry, in order to formulate their algorithmic needsprecisely and to make available algorithmic tools, insights fromtheoretical results, and software from experimental investigations.The specific repertoire of problems includes: (a) Geometric NetworkOptimization: optimal routing and network design in geometriccontexts, including traveling salesman (TSP) variants, vehiclerouting, constrained spanning trees, minimum-weight subdivisions,optimal route planning with various constraints, and survivablenetwork design; (b) Air Traffic Management: optimal use of airspacein the face of dynamic and uncertain constraints induced by weatherand traffic congestion, sectorization (load balancing), andoptimization of flow management structures for the National AirspaceSystem; (c) Sensor Networks and Coverage: sensor deployment,localization, data field monitoring, and coverage for stationary ormobile (robotic) sensors.The problems will be attacked on two fronts: (1) Use of formalalgorithmic analysis, attempting to prove the tightest possible bounds(upper and lower) on the worst-case or average-case time/space, orapproximation ratio for the problem; and (2) Development of solutiontechniques designed to be simple, fast, and practical, and which arecompared experimentally.

计算几何形状的方法将应用于设计，分析，实施和测试算法，以解决出现的Inseveral应用领域的问题，包括几何网络优化，空中交通管理，传感器网络，机器人技术，几何建模和制造。 主要项目目标是开发几何问题的近似算法的发展进步。 此外，该项目将努力与研究人员和应用程序中的研究人员和领域专家培养和深入验证，以制定其算法的需求，并提供算法工具，从理论结果中获得的见解，来自实验研究的软件以及问题的特定范围。旅行推销员（TSP）的变体，车辆划分，跨越树木的约束，最小重量细分，最佳路线规划具有各种限制，以及survivablablenetwork设计； （b）空中交通管理：空格的最佳用途是由天气和交通拥堵，部门化（负载平衡），国家空间系统的流量管理结构的动态和不确定限制的面孔； (c) Sensor Networks and Coverage: sensor deployment,localization, data field monitoring, and coverage for stationary ormobile (robotic) sensors.The problems will be attacked on two fronts: (1) Use of formalalgorithmic analysis, attempting to prove the tightest possible bounds(upper and lower) on the worst-case or average-case time/space, orapproximation ratio for the problem; （2）开发旨在简单，快速和实用的解决方案技术，并且在实验上具有截然不同的作用。