Ulf Rüegg

Compact Layered Drawings of General Directed Graphs

We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph \(G=(V,A)\) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number of reversed arcs, the arc lengths, and the width of the drawing. We call this the Compact Generalized Layering Problem (CGLP). Here, the width of a drawing is defined as the maximum sum of the number of vertices placed on a layer and the number of dummy vertices caused by arcs traversing the layer. The CGLP is \(\mathcal {NP}\)-hard. We present two MIP models for this problem. The first one (EXT) is our extension of a natural formulation for directed acyclic graphs as suggested by Healy and Nikolov. The second one (CGL) is a new formulation based on partial orderings. Our computational experiments on two benchmark sets show that the CGL formulation can be solved much faster than EXT using standard commercial MIP solvers. Moreover, we suggest a variant of CGL, called MML, that can be seen as a heuristic approach. In our experiments, MML clearly improves on CGL in terms of running time while it does not considerably increase the average arc lengths and widths of the layouts although it solves a slightly different problem where the dummy vertices are not taken into account.

A Generalization of the Directed Graph Layering Problem

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set Problem (FASP) to make the graph acyclic before a layering is determined.

HorusCML: Context-aware Domain-Specific Visual Languages Designer

The objective behind building domain-specific visual languages (DSVLs) is to provide users with the most appropriate concepts and notations that best fit with their domain and experience. However, the existing DSVL designers do not support integrating environment and user context information when modeling, editing or viewing DSVL models at different locations, permissions, devices, etc. In this paper, we introduce HorusCML, a context-aware DSVL designer, which supports DSVL experts in integrating necessary context details within their DSVLs. The resultant DSVLs can reflect different facets, layouts, and behaviours according to context it is used in. We show a case study on developing a context-aware data flow diagram DSVL tool using HorusCML.

Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports

We present a fundamentally different approach to orthogonal layout of data flow diagrams with ports. This is based on extending constrained stress majorization to cater for ports and flow layout. Because we are minimizing stress we are able to better display global structure, as measured by several criteria such as stress, edge-length variance, and aspect ratio. Compared to the layered approach, our layouts tend to exhibit symmetries, and eliminate inter-layer whitespace, making the diagrams more compact.

Generalized Layerings for Arbitrary and Fixed Drawing Areas

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set Problem (FASP) to make the graph acyclic before a layering is determined. Here we present the Generalized Layering Problem (GLP), which solves the combination of DLP and FASP simultaneously, allowing general graphs as input. We present an integer programming model and a heuristic to solve the NP-complete GLP and perform thorough evaluations on different sets of graphs and with different implementations for the steps of the layer-based approach. We observe that GLP reduces the number of dummy nodes significantly, can produce more compact drawings, and improves on graphs where DLP yields poor aspect ratios. The drawings resulting from GLP also turn out to be more suitable for making the best possible use of a given drawing area. However, we show that a specialized variant of GLP can yield considerable improvements w. r. t. this particular optimization goal.

Using One-Dimensional Compaction for Smaller Graph Drawings

We use the technique of one-dimensional compaction as part of two new methods tackling problems in the context of automatic diagram layout: First, a post-processing of the layer-based layout algorithm, also known as Sugiyama layout, and second a placement algorithm for connected components with external extensions. We apply our methods to dataflow diagrams from practical applications and find that the first method significantly reduces the width of left-to-right drawn diagrams. The second method allows to properly arrange disconnected graphs that have hierarchy-crossing edges.

Convert meets KIELER: Integrating advanced layout algorithms into by-example visualisations

The CONcrete Visual assistEd Transformation (CONVErT) framework provides facilities to generate reusable notations and compose them to form a wide variety of visualisations. With an increased number of notations in large scale visualisations, it is crucial to use advanced layout algorithms to improve understandability of such complex visualisations. This showpiece paper demonstrates how advanced layout algorithms can be integrated into the notation specifications of CONVErT to generate layouts of complex visualisations.

Counting Crossings for Layered Hypergraphs

Orthogonally drawn hypergraphs have important applications, e. g. in actor-oriented data flow diagrams for modeling complex software systems. Graph drawing algorithms based on the approach by Sugiyama et al. place nodes into consecutive layers and try to minimize the number of edge crossings by finding suitable orderings of the nodes in each layer. With orthogonal hyperedges, however, the exact number of crossings is not determined until the edges are actually routed in a later phase of the algorithm, which makes it hard to evaluate the quality of a given node ordering beforehand. In this paper, we present and evaluate two cross counting algorithms that predict the number of crossings between orthogonally routed hyperedges much more accurately than the traditional straight-line method.

Wrapping Layered Graphs

We present additions to the widely-used layout method for directed acyclic graphs of Sugiyama et al. that allow to better utilize a prescribed drawing area. The method itself partitions the graph’s nodes into layers. When drawing from top to bottom, the number of layers directly impacts the height of a resulting drawing and is bound from below by the graph’s longest path. As a consequence, the drawings of certain graphs are significantly taller than wide, making it hard to properly display them on a medium such as a computer screen without scaling the graph’s elements down to illegibility. We address this with the Wrapping Layered Graphs Problem (WLGP), which seeks for cut indices that split a given layering into chunks that are drawn side-by-side with a preferably small number of edges wrapping backwards. Our experience and a quantitative evaluation indicate that the proposed wrapping allows an improved presentation of narrow graphs, which occur frequently in practice and of which the internal compiler representation SCG is one example.

Incremental diagram layout for automated model migration

A range of successful modeling tools to develop complex systems use node-link-style diagrams as their underlying language. Over the years such languages can change, for instance as part of a tool update. When migrating existing models, changes in syntax directly affect the placement of elements in their diagrams. Increasing the size of certain nodes may for example result in node overlaps. In this paper we propose two methods based on graph drawing techniques to adjust the layout of existing diagrams after migration. Although we designed these techniques for diagram migration, they are applicable to other scenarios as well, such as users interactively adding or resizing nodes. We evaluate the techniques based on real world diagrams from the LabVIEW suite and discuss the scenarios each technique seems best suited for.