AF: Small: Approximation Algorithms for Uncertain Environments and Graph Partitioning

AF：小：不确定环境和图分区的近似算法

• 批准号: 1319811
• 负责人: Anupam Gupta
• 金额: $ 39.99万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1319811&HistoricalAwards=false
• 关键词: AF; Small; Approximation; Algorithms; Uncertain

This project focuses on research and teaching activities in the general area of approximation and online algorithms. Many optimization problems are intractable, so it is natural to approximate the optimum instead of computing an exact solution. With this insight, the past two decades have seen tremendous activity in approximation algorithms, to the point where the approximability of some basic problems is well-understood. In addition to this enhanced understanding of the computational complexity of optimization problems, an ever-increasing set of techniques and tools to attack problems old and new have been proposed. Given this situation, it is natural to take a two-pronged plan of research: while continuing to resolve some of the long-standing open problems of interest, the investigator will concurrently extend the scope of the new techniques, and also investigate more expressive models and problem abstractions that attempt to capture the rich diversity of optimization problems that arise in practice.Along these lines, a major theme of this research is to investigate how to solve optimization problems in the presence of partial information, and hence uncertainty. This is something often considered in practice: based only on probabilities of various events happening in the future, and subject to constraints on resources (time/money), a system must make decisions. In the spirit of computational thinking, this research is aimed at formalizing some of these problems so that efficient solutions can be found for more realistic models than the traditional worst-case model. Research progress on these questions will advance the state-of-the-art in decision-making under uncertainty, an area lying at the intersection of computer science, operations research, and decision theory. This research will also be instrumental in training of graduate and undergraduate students.

该项目专注于近似和在线算法的一般领域的研究和教学活动，许多优化问题都是棘手的，因此自然是近似最优解而不是计算精确解，在过去的二十年里。人们在近似算法方面进行了巨大的活动，以至于一些基本问题的近似性得到了很好的理解。除了对优化问题的计算复杂性的理解得到增强之外，解决旧问题的技术和工具也在不断增加。鉴于这种情况，自然要采取双管齐下的研究计划：在继续解决一些长期存在的感兴趣的开放问题的同时，研究者将同时扩大新技术的范围，并研究更具表现力的模型和问题抽象，试图捕捉实践中出现的优化问题的丰富多样性。沿着这些思路，本研究的一个主要主题是研究如何在存在部分信息的情况下解决优化问题，以及因此存在不确定性。这是实践中经常考虑的问题：仅基于未来发生的各种事件的概率，并受到资源（时间/金钱）的限制，系统必须本着计算思维的精神做出决策，本研究旨在形式化其中一些问题，以便提高效率。可以找到比传统最坏情况模型更现实的模型的解决方案，这些问题的研究进展将推动不确定性决策的最新技术，这是计算机科学和运筹学的交叉领域。和决策理论。研究生和本科生。