CAREER: Theoretical and Practical Solutions for Geometric Path Planning and Related Problems

职业：几何路径规划及相关问题的理论和实践解决方案

• 批准号: 9623585
• 负责人: Danny Chen
• 金额: $ 20万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-03-15 至 2001-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623585&HistoricalAwards=false
• 关键词: CAREER; Theoretical; Practical; Solutions; Geometric

9623585 Chen This project will study the design, analysis, and implementation of algorithmic techniques for solving geometric shortest path problems, their generalizations, and applications. Of interest are not only theoretically efficient algorithms, but also practically efficient ones. The research has three main interests: (a) Develop efficient algorithmic solutions for several fundamental geometric shortest path problems that are still outstanding (e.g., geometric shortest path queries), (b) investigate new approaches to computing approximate geometric shortest paths, and (c) design effective and practically efficient paradigms for planning robotic shortest paths in the plane and in higher dimensional spaces. Several general frameworks for processing exact and approximate geometric shortest path queries will be investigated. These frameworks offer the promise of achieving new efficient algorithmic techniques and data structures for geometric shortest path queries and for other related problems. Also, a paradigm is being studied for obtaining practical solutions to planning shortest obstacle-avoiding paths for robot motion in planar and higher dimensional environments. This paradigm is based on new data structures called framed-quadtrees and framed-octrees, and has led to new practical robotic path planning algorithms. In addition, algorithmic solutions for shortest paths and their generalizations are applied to practical applications such as data compression, computer vision, image processing, and VLSI design. New approaches for solving application problems based on algorithms for shortest path problems and their generalizations are studied. The possibility of finding new methods for geometric shortest paths that yield efficient implementation performance on existing Massively Parallel Processing (MPP) systems is also explored. The research also includes an important experimental component. The education plan is to develop a new environment for t eaching and experimenting with Massively Parallel Processing (MPP) systems by utilizing the new EXECUBE-based MPP architectures. The goal is to develop an inexpensive, but very robust, MPP system for upper level undergraduate and entry level graduate students to study and gain "hands on" experience with parallelism. The curriculum materials to be developed include concise programming tutorials, lecture notes, sample programs, and projects with sample solutions. This work could provide an integral part of not just electives in parallelism, but virtually of all the upper level computer science and engineering curriculum, and could even provide a basis to spill over into other engineering and scientific disciplines. ***

9623585 Chen 该项目将研究解决几何最短路径问题的算法技术的设计、分析和实现、其概括和应用。 令人感兴趣的不仅是理论上有效的算法，而且还有实践上有效的算法。 该研究有三个主要兴趣：（a）为仍然悬而未决的几个基本几何最短路径问题（例如几何最短路径查询）开发有效的算法解决方案，（b）研究计算近似几何最短路径的新方法，以及（c）设计有效且实用的范式，用于在平面和高维空间中规划机器人最短路径。 将研究用于处理精确和近似几何最短路径查询的几个通用框架。 这些框架有望为几何最短路径查询和其他相关问题实现新的高效算法技术和数据结构。 此外，正在研究一种范式，以获得在平面和高维环境中规划机器人运动的最短避障路径的实用解决方案。 该范例基于称为框架四叉树和框架八叉树的新数据结构，并导致了新的实用机器人路径规划算法。 此外，最短路径的算法解决方案及其推广应用于数据压缩、计算机视觉、图像处理和超大规模集成电路设计等实际应用。 研究了基于最短路径问题算法解决应用问题的新方法及其概括。 还探讨了寻找新的几何最短路径方法的可能性，这些方法可以在现有的大规模并行处理（MPP）系统上产生高效的实现性能。 该研究还包括一个重要的实验部分。 该教育计划旨在利用基于 EXECUBE 的新 MPP 架构开发一个新的环境，用于大规模并行处理 (MPP) 系统的教学和实验。 目标是开发一种廉价但非常强大的 MPP 系统，供高年级本科生和入门级研究生学习并获得并行性的“实践”经验。 待开发的课程材料包括简明编程教程、讲义、示例程序以及带有示例解决方案的项目。 这项工作不仅可以提供并行选修课的组成部分，而且可以提供几乎所有高级计算机科学和工程课程的组成部分，甚至可以为扩展到其他工程和科学学科提供基础。 ***