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

TL;DR

This paper presents a shape-first methodology for orthogonal graph drawings that prioritizes minimizing bends over crossings, using SAT solvers to handle rectilinear drawability and edge subdivision, leading to improved drawing quality.

Contribution

It introduces a novel approach that focuses on bend minimization and uses SAT solving for rectilinear drawability, challenging traditional crossing-focused algorithms.

Findings

Outperforms TSM-based methods in most metrics

Effectively uses SAT solvers for rectilinear drawability

Provides a practical implementation with extensive experiments

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.