Hypergraph models for complex discrete systems

复杂离散系统的超图模型

• 批准号: DP190100977
• 负责人: Prof Catherine Greenhill
• 金额: $ 29.25万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-05-08 至 2023-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190100977
• 关键词: Hypergraph; models; complex; discrete; systems

This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.

超图是一种非常普遍的数学对象，可以用来模拟复杂的离散系统。它们在生态学、化学和计算机科学等许多领域自然产生。尽管如此，我们对非常大的超图或随机超图的理论理解远远落后于图的特殊情况。这个项目将回答许多关于大型随机超图的基本问题。该项目的预期成果还包括用于处理超图的新工具，例如用于对超图进行采样的有效算法。这些成果将有利于在工作中使用超图的研究人员，并将提高澳大利亚在这一领域研究的声誉。