A Walk on the Wild Side: a Shape-First Methodology for Orthogonal Drawings

2025-08-26

AI Summary

Traditional orthogonal graph drawing prioritizes crossing minimization, often yielding layouts with excessively long edges, excessive bends, low compactness, and limited readability improvement from orthogonal crossings. Method: This paper proposes a “shape-first” paradigm that prioritizes bend minimization as the primary optimization objective, overturning the classical Topology–Shape–Metrics (TSM) pipeline. We formulate orthogonal drawability as a SAT problem for the first time, dynamically subdividing edges via virtual vertices and leveraging SAT solvers to determine optimal subdivision strategies; subsequent coordinate optimization produces compact, regular layouts. Contribution/Results: Our DOMUS algorithm significantly outperforms OGDF’s TSM implementation in bend count, drawing area compactness, and overall readability. It establishes a new geometrically intuitive and visually cognitively aligned approach to orthogonal graph drawing.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Several algorithms for the construction of orthogonal drawings of graphs, including those based on the Topology-Shape-Metrics (TSM) paradigm, tend to prioritize the minimization of crossings. This emphasis has two notable side effects: some edges are drawn with unnecessarily long sequences of segments and bends, and the overall drawing area may become excessively large. As a result, the produced drawings often lack geometric uniformity. Moreover, orthogonal crossings are known to have a limited impact on readability, suggesting that crossing minimization may not always be the optimal goal. In this paper, we introduce a methodology that 'subverts' the traditional TSM pipeline by focusing on minimizing bends. Given a graph $G$, we ideally seek to construct a rectilinear drawing of $G$, that is, an orthogonal drawing with no bends. When not possible, we incrementally subdivide the edges of $G$ by introducing dummy vertices that will (possibly) correspond to bends in the final drawing. This process continues until a rectilinear drawing of a subdivision of the graph is found, after which the final coordinates are computed. We tackle the (NP-complete) rectilinear drawability problem by encoding it as a SAT formula and solving it with state-of-the-art SAT solvers. If the SAT formula is unsatisfiable, we use the solver's proof to determine which edge to subdivide. Our implementation, DOMUS, which is fairly simple, is evaluated through extensive experiments on small- to medium-sized graphs. The results show that it consistently outperforms OGDF's TSM-based approach across most standard graph drawing metrics.

Problem

• Minimizing bends instead of crossings in orthogonal graph drawings
• Addressing unnecessarily long edge segments and large drawing areas
• Solving NP-complete rectilinear drawability via SAT encoding

Innovation

• Focuses on minimizing bends in orthogonal graph drawings
• Encodes rectilinear drawability as SAT formula for solving
• Subdivides edges incrementally using dummy vertices for bends