AI 中文总结
研究中小规模平面图绘制算法，比较既定算法、启发式算法及新优化方法，发现无算法在所有美学标准上最佳，优化单一属性常损另一属性，直接优化及分数引导组合效果较好，设计通用简单稳健算法仍是难题。
AI 中文摘要
平面图在图形绘制中至关重要，在平面布局及相关结构方面有大量成果。每个平面图都有平面直线图，算法能保证额外几何或组合性质。但不清楚哪种算法在实际中效果最佳。我们对中小规模平面图（10至400个顶点）的大型基准集进行平面图绘制算法实验评估。比较了图形绘制文献中的既定算法、实用的力导向和基于压力的启发式算法以及直接改善诸如边长均匀性、面面积平衡和角度分辨率等视觉属性的新的基于优化的方法。结果表明，没有一种评估算法在所有美学标准上都是最佳的，优化一种视觉属性往往会使另一种变差。直接优化视觉标准能提高目标分数，几种方法的分数引导组合能给出最佳综合结果，但没有简单算法成为明显通用的默认选择。因此，设计一种在不同图形家族和美学标准上都表现良好的简单、稳健算法仍是一个开放的实际问题。
英文摘要
Planar graphs are central to graph drawing, with extensive results on planar layouts and related structures. Every planar graph admits a planar straight-line drawing, and algorithms can guarantee additional geometric or combinatorial properties. However, it is unclear which algorithms work best in practice. Even for small graphs with near-perfect manual drawings, standard algorithms might produce poor spacing, distorted faces, or small angles. We present an experimental evaluation of planar graph drawing algorithms on a large benchmark collection of small and medium-sized planar graphs (\(10\)--\(400\) vertices). The study compares established algorithms from the graph drawing literature, practical force-directed and pressure-based heuristics, and new optimization-based methods that directly improve visual properties such as edge-length uniformity, face-area balance, and angular resolution. The results show that no evaluated algorithm is best across all aesthetic criteria, and optimizing one visual property often worsens another. Directly optimizing visual criteria improves targeted scores, and score-guided combination of several methods gives the best aggregate results, but no simple algorithm emerges as a clear universal default. Designing a simple, robust algorithm that performs well across graph families and aesthetic criteria therefore remains an open practical problem.
CommentsTo appear in the proceedings of the 34th International Symposium on Graph Drawing and Network Visualization (GD 2026)
