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VSAL: A Vision Solver with Adaptive Layouts for Graph Property Detection

Jiahao Xie, Guangmo Tong

TL;DR

VSAL is proposed, a vision-based framework that incorporates an adaptive layout generator capable of dynamically producing informative graph visualizations tailored to individual instances, thereby improving graph property detection.

Abstract

Graph property detection aims to determine whether a graph exhibits certain structural properties, such as being Hamiltonian. Recently, learning-based approaches have shown great promise by leveraging data-driven models to detect graph properties efficiently. In particular, vision-based methods offer a visually intuitive solution by processing the visualizations of graphs. However, existing vision-based methods rely on fixed visual graph layouts, and therefore, the expressiveness of their pipeline is restricted. To overcome this limitation, we propose VSAL, a vision-based framework that incorporates an adaptive layout generator capable of dynamically producing informative graph visualizations tailored to individual instances, thereby improving graph property detection. Extensive experiments demonstrate that VSAL outperforms state-of-the-art vision-based methods on various tasks such as Hamiltonian cycle, planarity, claw-freeness, and tree detection.

VSAL: A Vision Solver with Adaptive Layouts for Graph Property Detection

TL;DR

VSAL is proposed, a vision-based framework that incorporates an adaptive layout generator capable of dynamically producing informative graph visualizations tailored to individual instances, thereby improving graph property detection.

Abstract

Graph property detection aims to determine whether a graph exhibits certain structural properties, such as being Hamiltonian. Recently, learning-based approaches have shown great promise by leveraging data-driven models to detect graph properties efficiently. In particular, vision-based methods offer a visually intuitive solution by processing the visualizations of graphs. However, existing vision-based methods rely on fixed visual graph layouts, and therefore, the expressiveness of their pipeline is restricted. To overcome this limitation, we propose VSAL, a vision-based framework that incorporates an adaptive layout generator capable of dynamically producing informative graph visualizations tailored to individual instances, thereby improving graph property detection. Extensive experiments demonstrate that VSAL outperforms state-of-the-art vision-based methods on various tasks such as Hamiltonian cycle, planarity, claw-freeness, and tree detection.
Paper Structure (30 sections, 27 equations, 6 figures, 10 tables, 2 algorithms)

This paper contains 30 sections, 27 equations, 6 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Methodology
  5. VSAL Framework
  6. Layout Generation
  7. Layout Visualization
  8. Image Classification and Wrap-up
  9. Training Method
  10. Reference Layout
  11. Adversarial Training with Classification Feedback
  12. Experiments
  13. Settings
  14. Tasks and Datasets
  15. VSAL Settings
  16. ...and 15 more sections

Figures (6)

  • Figure 1: Each pair of (a)-(d) shows a simple graph with a certain property, including the adjacency matrix (left) and a well-designed layout generated by VSAL (right). Each pair of (e)-(g) shows a complex graph with a random layout (left) and a well-designed layout generated by VSAL (right).
  • Figure 2: Layout visualization process: (a) normalized coordinates, (b) node rendering, (c) edge rendering, and (d) Gaussian smoothing.
  • Figure 3: Each pair shows an example of the initial layout (top) and the refined layout (bottom) via Eq. \ref{['eq: refine']}.
  • Figure 4: Each pair illustrates graph layouts produced by VN-Solver (top) and VSAL (bottom) on the Ham. (a) and (b) show large graph layouts with circular and spiral layouts. (c) and (d) present the corresponding layouts for huge graphs.
  • Figure 5: Examples of graph layouts generated during the training of VSAL on the Hamiltonian cycle problem at a resolution of $224\times 224$. Each group shows four layouts generated after, respectively, 0, 5, 10, and 15 epochs, from left to right.
  • ...and 1 more figures