CAREER: Approximation Algorithms for Geometric Computing

职业:几何计算的近似算法

基本信息

项目摘要

0132901Har-Peled, SarielU of Ill, Urbana-ChampaignComputational geometry is the branch of theoretical computer science devoted to the design,analysis, and implementation of geometric algorithms and data structures. Computationalgeometry has deep roots in reality: Geometric problems arise naturally in any computa-tional field that simulates or interacts with the physical world|computer graphics, robotics,geographic information systems, computer aided-design, and molecular modeling, to namea few|as well as in more abstract domains such as combinatorial geometry and algebraictopology. Aside from their obvious practical significance, geometric algorithms and datastructures enjoy a rich and satisfying mathematical structure, and their development oftenrequires tools from mathematical disciplines such as combinatorics, topology, and algebraicgeometry, as well as traditional computational tools.The proposal outlines a challenging career development plan focusing on research in abroad cross-section of computational geometry, building on and significantly broadening thePI's successful work in the field over the last several years. Specific problem areas in whichthe PI plans to work include approximation algorithms, kinetic data structures, spatial andtemporal databases, external memory computation, geometric optimization, and clustering.This classification is at best a rough guide, as many interesting geometric problems fallinto more than one category. Furthermore, the PI plans to continue combining theory andempirical experimentation in his work, putting an emphasize on algorithms that performwell in practice.
0132901 Har-Peled,SarielU of Ill,Urbana-Champaign计算几何是理论计算机科学的分支,致力于设计、分析和实现几何算法和数据结构。计算几何在现实中有着深厚的根基:几何问题在任何模拟物理世界或与物理世界相互作用的计算领域中自然出现|计算机图形学、机器人技术、地理信息系统、计算机辅助设计和分子建模,仅举几例|以及在更抽象的领域,如组合几何和代数拓扑。几何算法和数据结构除了具有明显的实际意义外,还具有丰富而令人满意的数学结构,它们的发展往往需要组合学、拓扑学和代数几何等数学学科的工具,以及传统的计算工具。该提案概述了一个具有挑战性的职业发展计划,重点是研究国外计算几何的横截面,在过去几年里,PI在该领域的成功工作的基础上,PI计划工作的具体问题领域包括近似算法、动力学数据结构、空间和时间数据库、外部内存计算、几何优化和聚类。这种分类充其量只是一个粗略的指南,因为许多有趣的几何问题都属于不止一个类别。此外,PI计划继续在他的工作中将理论和实验结合起来,强调在实践中表现良好的算法。

项目成果

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Sariel Har-Peled其他文献

A replacement for Voronoi diagrams of near linear size
High-Dimensional Shape Fitting in Linear Time
  • DOI:
    10.1007/s00454-004-1118-2
  • 发表时间:
    2004-06-28
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Sariel Har-Peled;Kasturi R. Varadarajan
  • 通讯作者:
    Kasturi R. Varadarajan
Chapter 25 Duality
  • DOI:
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sariel Har-Peled
  • 通讯作者:
    Sariel Har-Peled
Shortest path in a polygon using sublinear space
  • DOI:
    10.20382/jocg.v7i2a3
  • 发表时间:
    2014-12
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sariel Har-Peled
  • 通讯作者:
    Sariel Har-Peled
Finding a Guard that Sees Most and a Shop that Sells Most
  • DOI:
    10.1007/s00454-007-1328-5
  • 发表时间:
    2007-05-01
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Otfried Cheong;Alon Efrat;Sariel Har-Peled
  • 通讯作者:
    Sariel Har-Peled

Sariel Har-Peled的其他文献

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{{ truncateString('Sariel Har-Peled', 18)}}的其他基金

NSF-BSF: AF: Small: New directions in geometric traversal theory
NSF-BSF:AF:小:几何遍历理论的新方向
  • 批准号:
    2317241
  • 财政年份:
    2023
  • 资助金额:
    $ 32.5万
  • 项目类别:
    Standard Grant
AF: Small: Towards Sturdier Geometric Algorithms
AF:小:迈向更坚固的几何算法
  • 批准号:
    1907400
  • 财政年份:
    2019
  • 资助金额:
    $ 32.5万
  • 项目类别:
    Standard Grant
AF: Small: Towards better geometric algorithms: Summarizing, partitioning and shrinking data
AF:小:迈向更好的几何算法:汇总、分区和缩小数据
  • 批准号:
    1421231
  • 财政年份:
    2014
  • 资助金额:
    $ 32.5万
  • 项目类别:
    Standard Grant
AF: Small: Efficient Proximity and Similarity Search in Computational Geometry
AF:小:计算几何中的高效邻近性和相似性搜索
  • 批准号:
    1217462
  • 财政年份:
    2012
  • 资助金额:
    $ 32.5万
  • 项目类别:
    Standard Grant
AF: Small: Approximation, Covering and Clustering in Computational Geometry
AF:小:计算几何中的近似、覆盖和聚类
  • 批准号:
    0915984
  • 财政年份:
    2009
  • 资助金额:
    $ 32.5万
  • 项目类别:
    Standard Grant

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