Geometric Computing

几何计算

基本信息

  • 批准号:
    RGPIN-2014-06399
  • 负责人:
  • 金额:
    $ 3.35万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2014
  • 资助国家:
    加拿大
  • 起止时间:
    2014-01-01 至 2015-12-31
  • 项目状态:
    已结题

项目摘要

My research area is Computational Geometry, a field devoted to the design and analysis of algorithms and data structures for geometric problems. My research focuses both on theoretical and practical issues. The geometric application areas I concentrate on include routing on geometric networks, geometric data structures, mesh generation/manipulation, graph drawing, visualization and pattern recognition. The main goal of my research has been and continues to be to bridge the gap between theoretical and practical efficiency by finding practical algorithmic solutions to applied geometric problems that have theoretical performance guarantees. Below, I provide a few examples of the type of geometric problems I am currently concentrating on. Communication between wireless devices has an inherent geometric component since these devices have a physical location which is constantly changing. Currently, I am applying my expertise in geometry to develop algorithms that take advantage of this geometric component resulting in more efficient and reliable communication between wireless devices. The problems in this area are particularly challenging since the network is dynamic, i.e. the wireless devices are usually moving. Moreover, this dynamic nature means that no single entity has complete knowledge of the whole network, requiring the development of algorithms that are online and use little memory. The standard method for modelling wireless networks is through the use of geometric graphs. A geometric graph is a graph where each vertex is a point in the plane (or possibly higher dimensions depending on the application) and an edge is a line segment or a curve joining two points. My research in this area focuses on the following themes: (1) How to route (i.e. find a path) efficiently in a geometric network, (2) How to construct geometric networks with certain desirable properties? Facility Location is an area where the main focus consists of placing one or more facilities in a region in a manner that optimizes certain criteria with respect to a set of clients. For example, in trying to decide where to build a new fire station in a city, one may want to place it somewhere that minimizes the response time to the target population. Facility Location problems are inherently geometric. Currently, I am studying several variants of this problem and trying to develop efficient solutions. A fundamental question in the manufacturing industry concerning every type of manufacturing process (such as NC-machining or casting) is: Given an object, can it be built using a particular process? I have successfully developed and applied computational geometry techniques to answer some basic problems of this type. Often it is geometric constraints that determine if an object can be built by a particular process. By modelling a process geometrically, we can determine if an object can be constructed at the design stage by determing if a CAD model of an object can be built by a particular manufacturing process. I plan to continue developing algorithms for answering these questions from a geometric perspective.
我的研究领域是计算几何,这是一个致力于设计和分析几何问题的算法和数据结构的领域。我的研究侧重于理论和实践问题。我关注的几何应用领域包括几何网络路由、几何数据结构、网格生成/操作、图形绘制、可视化和模式识别。我研究的主要目标一直是并将继续是通过寻找具有理论性能保证的应用几何问题的实用算法解决方案来弥合理论和实际效率之间的差距。下面,我将提供一些我目前正在关注的几何问题的例子。无线设备之间的通信具有固有的几何成分,因为这些设备具有不断变化的物理位置。目前,我正在运用我在几何方面的专业知识开发算法,利用这种几何组件,从而在无线设备之间实现更高效、更可靠的通信。这个领域的问题尤其具有挑战性,因为网络是动态的,即无线设备通常是移动的。此外,这种动态特性意味着没有一个实体对整个网络有完整的了解,这就需要开发在线的、占用很少内存的算法。无线网络建模的标准方法是使用几何图形。几何图形是这样一种图形,其中每个顶点是平面上的一个点(或者可能是更高的维度,取决于应用程序),而边是连接两点的线段或曲线。我在这一领域的研究主要集中在以下主题:(1)如何在几何网络中有效地路由(即找到路径);(2)如何构建具有某些理想性质的几何网络?设施选址是一个区域,主要关注的是在一个区域内以一种针对一组客户优化某些标准的方式放置一个或多个设施。例如,在试图决定在城市中何处建立新的消防站时,人们可能希望将其放置在对目标人群的响应时间最短的地方。设施选址问题本质上是几何问题。目前,我正在研究这个问题的几个变体,并试图找到有效的解决方案。制造业中涉及每种制造过程(如nc加工或铸造)的一个基本问题是:给定一个对象,它可以使用特定的过程来构建吗?我已经成功地开发和应用计算几何技术来回答这类问题的一些基本问题。通常是几何约束决定了一个物体是否可以通过特定的过程来构建。通过对一个过程进行几何建模,我们可以通过确定一个对象的CAD模型是否可以通过一个特定的制造过程来构建,从而确定一个对象是否可以在设计阶段被构建。我计划继续开发从几何角度回答这些问题的算法。

项目成果

期刊论文数量(0)
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Bose, Prosenjit其他文献

PROXIMITY GRAPHS: E, δ, Δ, χ AND ω
Switching to Directional Antennas with Constant Increase in Radius and Hop Distance
  • DOI:
    10.1007/s00453-012-9739-y
  • 发表时间:
    2014-06-01
  • 期刊:
  • 影响因子:
    1.1
  • 作者:
    Bose, Prosenjit;Carmi, Paz;Maheshwari, Anil
  • 通讯作者:
    Maheshwari, Anil
On plane geometric spanners: A survey and open problems
Space-efficient geometric divide-and-conquer algorithms
Area-preserving approximations of polygonal paths
  • DOI:
    10.1016/j.jda.2005.06.008
  • 发表时间:
    2006-12-01
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Bose, Prosenjit;Cabello, Sergio;Speckmann, Bettina
  • 通讯作者:
    Speckmann, Bettina

Bose, Prosenjit的其他文献

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{{ truncateString('Bose, Prosenjit', 18)}}的其他基金

Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2022
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Novel algorithms for improving manufacturing analytics
用于改进制造分析的新颖算法
  • 批准号:
    544092-2019
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Engage Grants Program
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric computing
几何计算
  • 批准号:
    204772-2009
  • 财政年份:
    2013
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual

相似海外基金

Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2022
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
EAGER: Hyperdimensional computing with geometric algebra
EAGER:几何代数的超维计算
  • 批准号:
    2147640
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Standard Grant
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Complexity of computing high dimensional volumes focusing on geometric duality
关注几何对偶性的高维体积计算的复杂性
  • 批准号:
    19K11832
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2019-06646
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
EAPSI: Comparison of Two Different Geometric Techniques for Computing Chemical Reaction Rates
EAPSI:计算化学反应速率的两种不同几何技术的比较
  • 批准号:
    1614377
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Fellowship Award
Geometric Computing
几何计算
  • 批准号:
    RGPIN-2014-06399
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
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