网络设计中的图论方法

In this project, we shall develop various mathematical methods including graph theory, combinatorial optimization, probabilistic method, group theory, spectral theory etc. to study reliability parameters which are closely related with fault-tolerant interconnection networks, rainbow connectivities which are closely related with security of big data in large scale networks, approximation algorithms for virtual backbones in wireless sensor networks which are closely related with efficient transmission of information and efficient utility of energy, and expander problems which are closely related with the design of communication networks and coding theory. Through the studies, we shall explore the role of graph theory in the design and analysis of networks, providing solid theoretical basis for the applications. At the same time, we shall explore new ideas and new methods in graph theory, enriching the contents and pushing the development of graph theory itself.

本项目将综合应用图论、组合优化、概率论、群论、谱理论等多种数学工具，研究与互联网络容错性密切相关的可靠性参数、与大数据网络安全性密切相关的彩虹连通数、与无线传感网络中高效的信息传输密切相关的虚拟骨干近似算法设计与分析、与通讯网络设计及编码理论密切相关的Expander问题。这四方面的研究各有侧重、相辅相成。通过上述研究，一方面充分挖掘图论方法在网络设计与分析中的功能，为实际应用提供可靠的理论保证；另一方面，探索图论领域的新思想、新方法，丰富图论自身理论的发展与进步。

本项目综合应用图论、组合优化、概率论、群论、谱理论等多种数学工具，研究了与互联网络容错性密切相关的可靠性参数、与大数据网络安全性密切相关的彩虹连通数、与无线传感网络中高效的信息传输密切相关的虚拟骨干近似算法设计与分析、与通讯网络设计及编码理论密切相关的Expander问题。在本项目的支持下，这四个方面的研究都按计划执行，并完成了全部的研究计划。除此之外，还在与本项目相关的研究中取得了一系列研究成果。这些研究成果不但为实际应用提供了理论保证，还丰富了图论自身理论的发展。