Combinatorial Designs and Graph Theory

组合设计和图论

• 批准号: RGPIN-2016-04456
• 负责人: Pike, David
• 金额: $ 1.6万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=662184
• 关键词: Combinatorial; Designs; Graph; Theory

Graphs, combinatorial block designs, and their properties are the central research areas of this research proposal. Graphs can often be viewed as networks with nodes and linkages between nodes. Designs are combinatorial structures that show how to form several subsets from a larger set so that certain properties are exhibited. Designs often have application in situations in which interactions need to take place. As an analogy, a teacher might encounter the scenario of having a class of students, each of whom must be assigned to several team projects so that each pair of students is on a team together the same number of times as every other pair of students. Different team assignments lead to designs with differing attributes, some of which are desirable but may be difficult to achieve. Moreover, how to go about scheduling the teams of a given design so that they satisfy certain constraints (especially so that consecutively scheduled teams have a specific number of people in common) is one of several questions that will be studied, often by investigating mathematical properties of graphs that are associated with designs. In addition to discovering new knowledge at the abstract level, the research will contribute to work being done in areas such as algorithms, scheduling, digital communications and others. The research will also provide advanced training opportunities for students, who will acquire experience in mathematical problem solving, technical writing, and programming with parallel computing. **

图、组合块设计及其属性是本研究提案的中心研究领域。 图通常可以被视为具有节点和节点之间的链接的网络。 设计是组合结构，展示如何从较大的集合中形成多个子集，以便展示某些属性。 设计通常适用于需要进行交互的情况。 打个比方，老师可能会遇到这样的情况：有一个班级的学生，每个学生必须被分配到几个团队项目，以便每对学生在一个团队中的次数与其他每对学生相同。 不同的团队分配导致设计具有不同的属性，其中一些是理想的，但可能难以实现。 此外，如何安排给定设计的团队，使其满足某些约束（尤其是连续安排的团队具有特定数量的共同点）是需要研究的几个问题之一，通常是通过研究与设计相关的图的数学属性来进行研究。 除了发现抽象层面的新知识外，该研究还将有助于算法、调度、数字通信等领域的工作。 该研究还将为学生提供高级培训机会，他们将获得数学问题解决、技术写作和并行计算编程的经验。 **