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

9623585 Chen本项目将研究几何最短路径问题的算法技术的设计、分析和实现，以及它们的推广和应用。 感兴趣的不仅是理论上有效的算法，而且是实际有效的算法。 该研究有三个主要兴趣：（a）为几个基本的几何最短路径问题开发有效的算法解决方案，这些问题仍然悬而未决（例如，几何最短路径查询），（B）研究计算近似几何最短路径的新方法，以及（c）设计用于规划平面和高维空间中的机器人最短路径的有效和实际高效的范例。 几个一般框架处理精确和近似的几何最短路径查询将进行调查。 这些框架为几何最短路径查询和其他相关问题提供了实现新的高效算法技术和数据结构的希望。 此外，一个范例正在研究获得实际的解决方案，规划最短的避障路径的机器人运动在平面和高维环境。 这种模式是基于新的数据结构称为框架四叉树和框架八叉树，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实际应用，如数据压缩，计算机视觉，图像处理和VLSI设计。 研究了基于最短路算法及其推广的解决应用问题的新方法。 几何最短路径，产生有效的执行性能在现有的大规模并行处理（MPP）系统找到新的方法的可能性也进行了探讨。 该研究还包括一个重要的实验组成部分。 该教育计划是利用新的基于EXECUBE的MPP体系结构开发一个新的教学和实验环境，用于大规模并行处理（MPP）系统。 我们的目标是开发一个廉价的，但非常强大的，MPP系统的上层本科生和入门级的研究生学习和获得“动手”的并行经验。 要开发的课程材料包括简明的编程教程、课堂讲稿、示例程序和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一个组成部分，而且几乎可以提供所有高级计算机科学和工程课程的一个组成部分，甚至可以提供一个基础，以溢出到其他工程和科学学科。 ***

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. ***