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.

该项目将试图改善线性编程领域的最新突破。 线性编程是用于优化的中心工具，用于物流，工厂规划，飞行计划以及许多其他任务。 最近，理论计算机科学家开发了线性编程算法，其性能比以前所知要好。 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此类向量上的功能行为。例如，向量可以与计划在飞行计划问题中从特定机场离开多少航班相对应。 该项目将严重涉及研究生设计更好的算法，并为本科生提供实施算法的机会。 PI一直与本科生合作，鉴于其实践影响的可能性，该项目特别适合包括本科生。伯克利计算机科学现在招募了来自文书和科学学院（除其工程学院的学生）的近900名学生，其中包含更大的女性。 PI特别有兴趣让该人群参与研究。这项项目努力提高复杂性并简化了最新的线性编程算法，尤其是最大流量问题。 线性编程问题是在空间中找到一个问题，该问题可以优化坐标上的线性函数并服从线性不等式。最大流量问题是一个特定的线性编程问题，人们希望将尽可能多的流通过网络推动。改进的想法是，在最大流量问题或可行的向量集的情况下，在线性编程的情况下，传统优化方法会更快地收敛。 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结合在一起。