Beyond Planarity: Algorithms for Visualisation of Sparse Non-Planar Graphs

该项目旨在开发新的高效算法，使分析师能够直观地理解复杂的数据并检测异常或模式。它的目标是为来自真实世界网络的稀疏非平面图开发可视化算法。具体地说，该项目计划研究稀疏非平面拓扑图的结构性质，如k-平面图、k-斜图、k-拟平面图，并设计高效的测试算法、嵌入算法和绘制算法。这些算法将通过现实世界的社交网络和生物网络进行评估。对组合结构和几何结构之间的数学相互作用的新见解将为新一代复杂网络可视化方法提供理论基础，该方法在社会网络、系统生物学、健康信息学、金融和安全方面具有潜在的应用。

This project aims to develop new efficient algorithms to enable analysts to visually understand complex data and detect anomalies or patterns. It aims to develop visualisation algorithms for sparse non-planar graphs arising from real-world networks. Specifically, the project plans to investigate structural properties of sparse non-planar topological graphs such as k-planar graphs, k-skew graphs, and k-quasi-planar graphs, and design efficient testing algorithms, embedding algorithms, and drawing algorithms. These algorithms will be evaluated with real-world social networks and biological networks. New insights into the mathematical interplay between combinatorial and geometric structures would provide a theoretical foundation for a new generation of complex network visualisation methods with potential applications in social networks, systems biology, health informatics, finance and security.