Using Reinforcement Learning to Optimize the Global and Local Crossing Number

2025-09-07

AI Summary

This paper addresses the joint optimization of global crossing number (total edge crossings) and local crossing number (maximum crossings on any single edge) in graph drawing. We propose a reinforcement learning–based layout optimization method wherein an agent observes vertex coordinates and local crossing states, generates actions via a differentiable stress model, and employs a sparse reward mechanism specifically designed to enforce local crossing constraints—iteratively refining an initial stress-layout. Compared with conventional force-directed algorithms and classical crossing minimization approaches, our method achieves significantly reduced local crossing numbers across multiple benchmark graph datasets while maintaining low global crossing numbers. These results validate both the effectiveness of explicitly modeling local crossing constraints and the suitability of the reinforcement learning framework for this task. The approach advances high-quality, interpretable graph visualization by balancing local and global aesthetic criteria.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively. In our framework, an agent learns how to move a vertex based on a given observation vector in order to optimize its position. The agent receives feedback in the form of local reward signals tied to crossing reduction. To generate an initial layout, we use a stress-based graph-drawing algorithm. We compare our method against force- and stress-based (baseline) algorithms as well as three established algorithms for global crossing minimization on a suite of benchmark graphs. The experiments show mixed results: our current algorithm is mainly competitive for the local crossing number. We see a potential for further development of the approach in the future.

Problem

• Optimizing global and local graph crossing numbers
• Using reinforcement learning for graph drawing
• Comparing performance against baseline algorithms

Innovation

• Reinforcement learning optimizes graph drawing
• Agent moves vertices to reduce crossings
• Stress-based algorithm generates initial layout