ITR: A New Computational Paradigm: Robustness as a Resource

ITR：新的计算范式：作为资源的鲁棒性

• 批准号: 0082056
• 负责人: Chee Yap
• 金额: $ 48.99万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0082056&HistoricalAwards=false
• 关键词: ITR; New; Computational; Paradigm; Robustness

The problem of numerical robustness and geometric consistency is well knownin many areas of computational science. The issue is that inexact computer arith-metic leads to incorrect and inconsistent geometric conclusions (for example, is apoint inside or outside a triangle). While computers are getting faster, softwareis not getting more robust. Indeed, the trend is towards more nonrobustness. Wepropose a new computational paradigm to reverse this trend.Robustness is often seen as an all-or-nothing proposition. Our new paradigmconsists in viewing robustness as a computational resource, to be traded off againstother resources such as speed. Each program defines a certain robustness-speedtrade-off curve; we want to be able to run the program at any point along thiscurve. This proposal will develop the technology to make this capability effcientand easily accessible to all programmers. As a result, any programmer can producenearly ordinary C/C++ code which can be run robustly. The implications of thisparadigm are wide ranging, and will bring the fruits of robustness research intomainstream computing.We propose to (1) conduct basic research to support this new computingparadigm, (2) to create the technology and software tools to achieve this paradigm,and (3) to explore the applications of fast and usually robust algorithms in algo-rithm design. For (1), we will focus on effciency issues such as novel root bounds,incremental computation, guaranteed absolute precision for elementary functions.For (2), we expect to significantly extend the power, efficiency and usability of ourCore Library and include capabilities such as symbolic perturbation. Finally anexample of (3) concerns the general problem of checking of geometric structures andtheir applications in new efficient geometric algorithms.We propose to apply our robustness techniques and software to two significantapplications in which nonrobustness problems are well-known:* Mesh Generation: we will construct the first fully robust mesh generator whichwill be deployed in a major ow solver system, Cart3d.* Geometric Modeling: we will build a robust geometric modeler which will bethe first such system that is precision-sensitive.This proposal involves international collaboration with Professor Mehlhorn'sAlgorithms and Complexity Group at the Max-Planck Institute of Computer Sci-ence in Germany. Our domestic collaborator are Michael Aftosmis from NASAAmes Research Center (on mesh generation) and Shankar Krishnan from AT&TResearch Laboratories (on geometric modeling).

数值鲁棒性和几何一致性问题在计算科学的许多领域是众所周知的。问题在于，不精确的计算机算术会导致不正确且不一致的几何结论（例如，点是在三角形内部还是外部）。虽然计算机变得越来越快，但软件并没有变得更加强大。事实上，趋势是变得更加不稳健。我们提出了一种新的计算范式来扭转这一趋势。鲁棒性通常被视为一个全有或全无的命题。我们的新范式将稳健性视为一种计算资源，需要与速度等其他资源进行权衡。每个程序都定义了一定的鲁棒性-速度权衡曲线；我们希望能够在这条曲线上的任何一点运行该程序。该提案将开发一项技术，使所有程序员都能高效且轻松地使用此功能。因此，任何程序员都可以生成可以稳健运行的几乎普通的 C/C++ 代码。这个范式的影响是广泛的，并将把鲁棒性研究的成果带入主流计算。我们建议（1）进行基础研究来支持这个新的计算范式，（2）创建实现这个范式的技术和软件工具，以及(3) 探索快速且鲁棒的算法在算法设计中的应用。对于（1），我们将重点关注效率问题，例如新颖的根界限、增量计算、保证初等函数的绝对精度。对于（2），我们期望显着扩展我们核心库的功能、效率和可用性，并包括以下功能作为象征性扰动。最后（3）的一个例子涉及几何结构检查的一般问题及其在新的高效几何算法中的应用。我们建议将我们的鲁棒性技术和软件应用于非鲁棒性问题众所周知的两个重要应用：*网格生成：我们将构建第一个完全鲁棒的网格生成器，它将部署在主要的流求解器系统 Cart3d 中。* 几何建模：我们将构建一个鲁棒的几何建模器，这将是第一个对精度敏感的系统。该提案涉及与德国马克斯普朗克计算机科学研究所 Mehlhorn 教授的算法和复杂性小组。我们的国内合作者是来自 NASAAmes 研究中心的 Michael Aftosmis（网格生成）和来自 AT&T 研究实验室的 Shankar Krishnan（几何建模）。