Orthogonal drawings of graphs with vertex and edge labels

Binucci, Carla; Didimo, Walter; Liotta, Giuseppe; Nonato, Maddalena

doi:10.1016/j.comgeo.2005.02.001

Cited by 16 publications

(20 citation statements)

References 13 publications

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“…This would also remove the current restriction (of 8) on the maximum vertex degree of the underlying subway graph. Some of this work can already be seen in the MIP formulation of Binucci et al [6], where vertices and labels are represented by axisparallel rectangles-for drawing graphs orthogonally.…”

Section: Discussionmentioning

confidence: 98%

“…A label at an interchange station is modeled individually as a special edge of length equal to the label length, see e.g., station Karlsplatz in Figure 11(e). Binucci et al [6] use a similar idea to label edges with rectangles in orthogonal graph drawings. In contrast to Nöllenburg and Wolff, Binucci et al consider each edge and its label individually.…”

Section: Label Placementmentioning

confidence: 99%

“…Klau and Mutzel [17] and Binucci et al [6] have used MIP formulations for graph labeling before. However, their methods follow Tamassia's topology-shape-metrics approach [34], which is a common approach for drawing graphs orthogonally.…”

Section: Introductionmentioning

confidence: 99%

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Drawing Subway Maps: A Survey

Wolff

2007

Informatik Forsch. Entw.

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This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also diagonals. This gives more flexibility in the layout process, but it also makes the problem provably hard. Second, a subway map represents a network whose components have geographic locations that are roughly known to the users of such a map. This knowledge must be respected during the search for a clear layout of the network. For the sake of visual clarity the underlying geography may be distorted, but it must not be given up, otherwise map users will be hopelessly confused.In this paper we first give a rather generally accepted list of rules that should be adhered to by a good subway map. Next we survey three recent methods for drawing subway maps, analyze their performance with respect to the above rules, and compare the resulting maps among each other and to official subway maps drawn by graphic designers. We then focus on one of the methods, which is based on mixed-integer linear programming, a widely-used global optimization technique. This method guarantees to find a drawing that fulfills a subset of the above-mentioned rules (if such a drawing exists) and optimizes a weighted sum of costs that correspond to the remaining rules. The method can draw even large subway networks such as the London Underground in an aesthetically pleasing manner, similar to maps made by professional graphic designers. If station labels are included in the optimization process, so far only mediumsize networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).

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Section: Discussionmentioning

confidence: 98%

Section: Label Placementmentioning

confidence: 99%

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Drawing Subway Maps: A Survey

Wolff

2007

Informatik Forsch. Entw.

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“…The former approach is obviously less restricted and has the potential to yield better results, but because every type of graph or layout style might require a different method of integrating labeling into layout, it is not widely studied [1,2,21]. The latter approach, however, has received much attention over the past decade.…”

Section: Automatic Label Placementmentioning

confidence: 99%

On labeling in graph visualization

Doğrusöz¹,

Kakoulis²,

Madden³

et al. 2007

Information Sciences

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When visualizing graphs, it is essential to communicate the meaning of each graph object via text or graphical labels. Automatic placement of labels in a graph is an NP-Hard problem, for which efficient heuristic solutions have been recently developed. In this paper, we describe a general framework for modeling, drawing, editing, and automatic placement of labels respecting user constraints. In addition, we present the interface and the basic engine of the Graph Editor Toolkit -a family of portable graph visualization libraries designed for integration into graphical user interface application programs. This toolkit produces a high quality automated placement of labels in a graph using our framework. A brief survey of automatic label placement algorithms is also presented. Finally we describe extensions to certain existing automatic label placement algorithms, allowing their integration into this visualization tool.

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“…Klau and Mutzel [35] gave an ILP formulation for the compaction phase in the topology-shape-metrics framework (see Appendix A) that minimizes the total edge length of the drawing subject to certain shape constraints and the placement of non-overlapping vertex labels. Binucci et al [36] gave a MIP formulation to minimize the area in the compaction phase in the presence of vertex and edge labels.…”

Section: Related Workmentioning

confidence: 99%

Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming

Nöllenburg

Wolff

2011

IEEE Trans. Visual. Comput. Graphics

134

167

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Abstract-Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing metro maps. There are two aspects to this problem that depend on each other: the layout problem of finding station and link coordinates and the labeling problem of placing non-overlapping station labels. In this paper we present a new integral approach that solves the combined layout and labeling problem (each of which, independently, is known to be NP-hard) using mixed-integer programming (MIP). We identify seven design rules used in most real-world metro maps. We split these rules into hard and soft constraints and translate them into a MIP model. Our MIP formulation finds a metro map that satisfies all hard constraints (if such a drawing exists) and minimizes a weighted sum of costs that correspond to the soft constraints. We have implemented the MIP model and present a case study and the results of an expert assessment to evaluate the performance of our approach in comparison to both manually designed official maps and results of previous layout methods.

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Orthogonal drawings of graphs with vertex and edge labels

Cited by 16 publications

References 13 publications

Drawing Subway Maps: A Survey

Drawing Subway Maps: A Survey

On labeling in graph visualization

Drawing and Labeling High-Quality Metro Maps by Mixed-Integer Programming

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