Collaborative Research: MSPA-MCS: Embeddings of Finite Metric Spaces - A Geometric Approach to Efficient Algorithms

合作研究：MSPA-MCS：有限度量空间的嵌入 - 高效算法的几何方法

• 批准号: 0528414
• 负责人: Sanjeev Arora
• 金额: $ 29万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0528414&HistoricalAwards=false
• 关键词: Collaborative; Research; MSPA; MCS; Embeddings

Geometry has become a central notion in algorithm design, in fieldsas diverse as bioinformatics and graph partitioning.This research is a concerted and unified attack on a large subset of theunderlying mathematical problems, which often have to do withgeometric embeddings of finite metric spaces.The concrete applications range from clustering and learning tocompact representation of data to graph partitioning tonearest neighbor searching. Since the research spans aa variety of fields, the assembled team is multidisciplinary,involving analysts (Johnson and Naor), a geometer (Gromov),a discrete mathematician and combinatorialist (Linial)and algorithm designers (Arora and Charikar).The research area emerging from the ongoing geometrization ofalgorithms is an exciting new frontier for both mathematics andcomputer science. For example, deep mathematical results such asLipschitz extension may turn out to have applicationsto the practical problem of compactly representing computer sounds.In turn, algorithmic settings provide a fertile new ground formathematical theory. The investigators study geometric representationsfor data and low disortion mappings into structured spaces. Metrics thatarise in the design of approximation algorithms for NP-hard problems arestudied, especially to understand their local versus global properties.The research develops new understanding for practicallyimportant metrics such as earth mover and edit distancemetrics, which are defined in terms of computational effort and havethus not been studied in mathematics.

几何形状已成为算法设计中的一个中心概念，在多样化的田地和图形分配中。这项研究是对大量数学问题子集的一致和统一的攻击，通常必须与有限度量的有限次数的几端嵌入相连的相邻应用程序范围内的范围绘制构成数据的范围来绘制数据的范围，从而构成了数据构成数据的范围。由于研究跨越了各种领域，因此组装的团队是多学科的，涉及分析师（Johnson and Naor），地理表（Gromov），一个离散的数学家和组合主义者和组合主义者（外线）和算法设计师（Arora和Charikar）。 科学。例如，aslipschitz扩展的深度数学结果可能会发现应用程序的实用问题，即紧凑型计算机声音。在转弯时，算法设置提供了一种肥沃的新地面构思理论。研究人员研究了对结构化空间的数据和低灾害映射的几何表示。在设计NP硬问题问题的近似算法中，尤其是为了了解其本地属性与全球属性的近似算法的指标，这项研究对实际上重要的指标有了新的理解，例如地球推动者和编辑远程计量学，这些指标是根据计算工作定义的，而不是在数学上都未经计算工作和Havethus进行了研究。