Graph Visualization, also known as Graph Drawing, aims to find geometric
embeddings of graphs that optimize certain criteria. Stress is a widely used
metric; stress is minimized when every pair of nodes is positioned at their
shortest path distance. However, stress optimization presents computational
challenges due to its inherent complexity and is usually solved using
heuristics in practice. We introduce a scalable Graph Neural Network (GNN)
based Graph Drawing framework with sub-quadratic runtime that can learn to
optimize stress. Inspired by classical stress optimization techniques and
force-directed layout algorithms, we create a coarsening hierarchy for the
input graph. Beginning at the coarsest level, we iteratively refine and
un-coarsen the layout, until we generate an embedding for the original graph.
To enhance information propagation within the network, we propose a novel
positional rewiring technique based on intermediate node positions. Our
empirical evaluation demonstrates that the framework achieves state-of-the-art
performance while remaining scalable.

图可视化，也称为图绘制，旨在找到优化特定标准的图形嵌入。本文介绍了一种基于可学习的子二次运行时的可缩放图神经网络（GNN）的图绘制框架，可以学习优化应力，并提出了一种基于中间节点位置的新型位置重连技术，实现了最先进的性能。

CoRe-GD: 可扩展图可视化的层次框架与 GNNs

CoRe-GD: A Hierarchical Framework for Scalable Graph Visualization with  GNNs

In contrast to the literature where local patterns in 3D point clouds are
captured by customized convolutional operators, in this paper we study the
problem of how to effectively and efficiently project such point clouds into a
2D image space so that traditional 2D convolutional neural networks (CNNs) such
as U-Net can be applied for segmentation. To this end, we are motivated by
graph drawing and reformulate it as an integer programming problem to learn the
topology-preserving graph-to-grid mapping for each individual point cloud. To
accelerate the computation in practice, we further propose a novel hierarchical
approximate algorithm. With the help of the Delaunay triangulation for graph
construction from point clouds and a multi-scale U-Net for segmentation, we
manage to demonstrate the state-of-the-art performance on ShapeNet and PartNet,
respectively, with significant improvement over the literature. Code is
available at this https URL

本文研究了点云数据如何被有效和高效地投影到 2D 图像空间中，以便于利用传统的 2D 卷积神经网络进行分割，通过引入具有拓扑结构保持特性的图形处理方法，并使用分层逼近算法，结合 Delaunay 三角剖分技术和多尺度 U-Net 网络进行图像分割，取得了 ShapeNet 和 PartNet 的最新成果。