Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
基本信息
- 批准号:170220-2011
- 负责人:
- 金额:$ 0.73万
- 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:2015
- 资助国家:加拿大
- 起止时间:2015-01-01 至 2016-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Combinatorial Designs provide an ideal way to understand the interaction properties of complex discrete structures, such as networks; a way to investigate the `interconnectedness' properties of such structures. The central focus of the proposed research program is the investigation of the structure of combinatorial designs; to consider designs with a particular structure, or lack thereof. Development in this area will provide a deeper understanding of the structure of the objects involved as well as insight into other combinatorial questions. Designs have well-known applications to statistics, coding theory and scheduling, in addition, there are potential applications to such diverse questions as algorithmic efficiency, software and network testing and numerical analysis. I have long been involved with finding various kinds of factorizations, initially uniform and class-uniformly resolvable designs, broadening this work to include more general factorizations, most notably cycle factorizations. I have also considered cases where factorization is not possible. More recently, I have become interested in Covering Arrays. This project will support my work in all of these areas.
The longstanding Oberwolfach problem, introduced by Ringel in the 1960s as a seating problem has recieved much attention over the years, with several recent advances. The more general Hamilton-Waterloo problem requires a factorization of the complete graph into a variety of cycle types. One of the objectives of this project is to continue investigation into these problems. Another goal is to undertake a consideration of combinatorial objects which fail to have a particular structure, such as resolvability.
Covering arrays have received much interest of late due to their applications in testing, particularly software and network testing. One of the goals of this proposal is to further investigate these objects, particularly with respect to substructures useful for testing that they may exhibit. This includes, mixed strength covering arrays and covering arrays with forbidden pairs or other configurations as well as the development, together with collaborators, of an online resource for generation of covering arrays, an important industrial resource.
组合设计提供了一种理想的方式来理解复杂的离散结构,如网络的相互作用特性;一种方法来研究这种结构的“互连性”特性。 拟议的研究计划的中心焦点是组合设计的结构的调查;考虑具有特定结构的设计,或缺乏。在这一领域的发展将提供一个更深入的了解所涉及的对象的结构,以及洞察到其他组合问题。设计有众所周知的应用统计,编码理论和调度,此外,有潜在的应用,如算法效率,软件和网络测试和数值分析等不同的问题。我一直致力于寻找各种类型的因子分解,最初是均匀的和类一致可分解的设计,将这项工作扩展到包括更一般的因子分解,最著名的是循环因子分解。我还考虑了不可能进行因式分解的情况。最近,我对覆盖数组产生了兴趣。这个项目将支持我在所有这些领域的工作。
长期存在的Oberwolfach问题,由Ringel在20世纪60年代引入作为一个座位问题,多年来一直受到关注,最近有几个进展。 更一般的哈密尔顿-滑铁卢问题需要将完全图分解为各种循环类型。该项目的目标之一是继续调查这些问题。另一个目标是考虑组合对象不能具有特定的结构,如可分解性。
覆盖阵列由于其在测试中的应用,特别是在软件和网络测试中的应用,最近受到了广泛的关注。本提案的目标之一是进一步研究这些对象,特别是关于它们可能展示的用于测试的子结构。这包括混合强度覆盖阵列和具有禁止对或其他配置的覆盖阵列,以及与合作者一起开发用于生成覆盖阵列的在线资源,这是一种重要的工业资源。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Danziger, Peter其他文献
Danziger, Peter的其他文献
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{{ truncateString('Danziger, Peter', 18)}}的其他基金
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2022-03816 - 财政年份:2022
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2021
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2020
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2019
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2018
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2017
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in Designs, Coverings and Decompositions
设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2016
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
- 批准号:
170220-2011 - 财政年份:2014
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
- 批准号:
170220-2011 - 财政年份:2013
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
- 批准号:
170220-2011 - 财政年份:2012
- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
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Structure in Designs, Coverings and Decompositions
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$ 0.73万 - 项目类别:
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设计、覆盖和分解的结构
- 批准号:
RGPIN-2016-04178 - 财政年份:2017
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$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
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设计、覆盖和分解的结构
- 批准号:
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- 资助金额:
$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
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设计、覆盖和分解的结构
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170220-2011 - 财政年份:2014
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$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
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$ 0.73万 - 项目类别:
Discovery Grants Program - Individual
Structure in designs, coverings and decompositions
设计、覆盖和分解的结构
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$ 0.73万 - 项目类别:
Discovery Grants Program - Individual