AI 中文总结
研究有序集线图节点标注问题，提出两阶段灵活算法，先过滤固定位置模型，利用空间处理溢出标签，通过成本函数和基于力的步骤平衡质量与运行时间，还应用于FCA领域展示灵活性。
AI 中文摘要
我们提出了一种灵活的两阶段算法来标注有序集的线图，其中序关系中直接相邻的节点由向上的直线连接。与任意图的图标注不同，有序集线图中的所有边或多或少是垂直的。我们研究所有标签的放置，使其不与任何节点、线或其他标签相交，同时最小化节点与其标签之间的距离。我们的方法首先使用线图特定的可读性标准过滤固定位置模型。对于不能紧邻其节点放置的标签（溢出标签），我们利用图内部的自由空间或绘图周围的无限空间，并通过直线连接线将标签与其各自的节点相连，连接线应尽可能不与其他节点或标签交叉。为了平衡质量和运行时间，我们使用候选稀疏网格上的成本函数得出溢出标签的初始放置，随后进行基于力的细化步骤来微调布局。此外，我们将此方法应用于形式概念分析（FCA）领域中线图的视觉约束，展示了该方法的灵活性，在FCA中某些标签必须放置在其节点上方，其他标签放置在下方。该算法的这个特殊版本表明，在第一阶段进行预过滤以及对成本函数和基于力的模型进行最小调整足以处理概念格所需的双重标注要求。
英文摘要
We propose a flexible, two-phase algorithm for labeling line diagrams of ordered sets, in which the nodes of direct neighbors in the order relation are connected by a straight, upward-pointing line. In contrast to the labeling of diagrams of arbitrary graphs, we benefit from the fact that all edges in line diagrams of ordered sets are more or less vertical. In this paper, we study the placement of all labels such that they do not intersect with any nodes, lines, or other labels while minimizing the distances between the nodes and their labels. Our approach starts by filtering the fixed-position model using line diagram-specific readability criteria. For labels that cannot be placed adjacent to their node (overflow labels), we exploit the free space in the graph's interior or the infinite space surrounding the drawing and link the labels with their respective node by straight binding lines that should not cross other nodes or labels if possible. To balance quality and runtime, we derive an initial placement of the overflow labels using a cost function over a sparse grid of candidates, followed by a force-based refinement step to fine-tune the layout. Furthermore, we demonstrate the flexibility of this approach by applying it to the visual constraints of line diagrams in the field of Formal Concept Analysis (FCA), where certain labels have to be placed above their node and others below. This special version of the algorithm shows that a pre-filtering in the first phase and minimal adjustments for the cost function and force-based model are sufficient to handle the dual labeling requirements of concept lattices.
CommentsTo appear in Proc. 34th International Symposium on Graph Drawing and Network Visualization (GD 2026)
