AF: Small: Algorithms: approximate, combinatorial, and continuous.

AF：小：算法：近似、组合和连续。

• 批准号: 1528174
• 负责人: Satish Rao
• 金额: $ 45万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1528174&HistoricalAwards=false
• 关键词: AF; Small; Algorithms; approximate; combinatorial

This project will attempt to improve recent breakthroughs in the area of linear programming. Linear programming is a central tool for optimization that is used in logistics, factory planning, flight scheduling, and numerous other tasks. Recently, theorical computer scientists have developed algorithms for linear programming with provably better performance than previously known. These algorithms rely on new understanding of basic mathematical objects such as vectors and measures of their length, and the behavior of functions on such vectors; the vectors could correspond, for example, to how many flights are scheduled to leave from a particular airport in a flight scheduling problem. The project will critically involve graduate students in designing provably better algorithms and will provide for opportunities for undergraduates in implementing the algorithms. The PI has consistently worked with undergraduates and this project, given its possibilities for practical impact, is especially well suited for the inclusion of undergraduate students. Berkeley Computer Science now enrolls almost 900 students from the College of Letters and Science (in addition to its College of Engineering Students) which contains a much larger fraction of women. The PI is especially interested in involving this population in research.This project endeavors to improve the complexity and simplify recent algorithms for linear programming and, in particular, the maximum flow problem. The linear programming problem is the problem of finding a point in space that optimizes a linear function on the coordinates and obeys linear inequalities. The maximum flow problem is a particular linear programming problem where one wishes to push as much flow through a network as possible. The idea of the improvement is to find alternate representations of the networks, in the case of the maximum flow problem, or the set of feasible vectors, in the case of linear programming, where traditional optimization methods converge faster. The methods combine a calculus based minimization approach with methods for efficiently capturing properties of networks and polytopes.

该项目将尝试改进线性规划领域的最新突破。 线性规划是优化的核心工具，可用于物流、工厂规划、航班调度和许多其他任务。 最近，理论计算机科学家开发了线性规划算法，其性能比以前已知的要好。 这些算法依赖于对基本数学对象的新理解，例如向量及其长度的度量，以及这些向量上的函数的行为；例如，向量可以对应于航班调度问题中计划从特定机场起飞的航班数量。 该项目将重点让研究生参与设计可证明更好的算法，并将为本科生提供实现算法的机会。 PI 一直与本科生合作，鉴于其实际影响的可能性，该项目特别适合本科生的参与。伯克利计算机科学学院目前招收了来自文学与科学学院（以及工程学院学生）的近 900 名学生，其中女性比例要高得多。 PI 对让这一群体参与研究特别感兴趣。该项目致力于提高线性规划（特别是最大流问题）的复杂性并简化最新算法。 线性规划问题是在空间中找到一个点来优化坐标上的线性函数并服从线性不等式的问题。最大流量问题是一种特殊的线性规划问题，人们希望通过网络推送尽可能多的流量。改进的想法是在最大流问题的情况下找到网络的替代表示，或者在线性规划的情况下找到可行向量的集合，其中传统优化方法收敛得更快。 这些方法将基于微积分的最小化方法与有效捕获网络和多面体属性的方法相结合。