Cologne Excellence Cluster on Cellular Stress Responses in Aging Associated Diseases
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Manhattan-Geodesic Embedding of Planar Graphs
No full textIn this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains of axis-parallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic embeddability on the grid is equivalent to 1-bend embeddability on the grid. For the latter question an efficient algorithm has been proposed. Second, we consider geodesic point-set embeddability where the task is to decide whether a given graph can be embedded on a given point set. We show that this problem is N P-hard. In contrast, we efficiently solve geodesic polygonization—the special case where the graph is a cycle. Third, we consider geodesic point-set embeddability where the vertex–point correspondence is given. We show that on the grid, this problem is N P-hard even for perfect matchings, but without the grid restriction, we solve the matching problem efficiently
Port Constraints in Hierarchical Layout of Data Flow Diagrams
No full textWe present a new application for graph drawing in the context of graphical model-based system design, where manual placing of graphical items is still state-of-the-practice. The KIELER framework aims at improving this by offering novel user interaction techniques, enabled by automatic layout of the diagrams. In this paper we present extensions of the well-known hierarchical layout approach, originally suggested by Sugiyama et al. to support port constraints, hyperedges, and compound graphs in order to layout diagrams of data flow languages. A case study and experimental results show that our algorithm is well suited for application in interactive user interfaces
Fast Edge-Routing for Large Graphs
No full textTo produce high quality drawings of graphs with nodes drawn as shapes it is important to find routes for the edges which do not intersect node boundaries. Recent work in this area involves finding shortest paths in a tangent-visibility graph. However, construction of the full tangent-visibility graph is expensive, at least quadratic time in the number of nodes. In this paper we explore two ideas for achieving faster edge routing using approximate shortest-path techniques
Drawing 3-Polytopes with Good Vertex Resolution
No full textWe study the problem how to obtain a small drawing of a 3-polytope with Euclidean distance between any two points at least 1. The problem can be reduced to a one-dimensional problem, since it is sufficient to guarantee distinct integer x-coordinates. We develop an algorithm that yields an embedding with the desired property such that the polytope is contained in a 2(n − 2) × 1 × 1 box. The constructed embedding can be scaled to a grid embedding whose x-coordinates are contained in [0, 2(n − 2)]. Furthermore, the point set of the embedding has a small spread, which differs from the best possible spread only by a multiplicative constant
3D Visibility Representations by Regular Polygons
No full textWe study 3D visibility representations of complete graphs where vertices are represented by equal regular polygons lying in planes parallel to the xy-plane. Edges correspond to the z-parallel visibility among these polygons. We improve the upper bound on the maximum size of a complete graph with a 3D visibility representation by regular n-gons from 2O(n) to O(n4 )
DAGmaps and ε-Visibility Representations of DAGs
No full textDAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NP-complete. Recently we defined a special case called one-dimensional DAGmap where the admissibility is decided in linear time. However there is no complete characterization of the class of DAGs that admit a onedimensional DAGmap. In this paper we prove that a DAG admits a one-dimensional DAGmap if and only if it admits a directed ε-visibility representation. Then we give a characterization of the DAGs that admit directed ε-visibility representations. Finally we show that a DAGmap defines a directed three-dimensional ε-visibility representation of a DAG. Keywords: DAGmap, Treemap, DAG, Visibility
On Open Problems in Biological Network Visualization
No full textMuch of the data generated and analyzed in the life sciences can be interpreted and represented by networks or graphs. Network analysis and visualization methods help in investigating them, and many universal as well as specialpurpose tools and libraries are available for this task. However, the two fields of graph drawing and network biology are still largely disconnected. Hence, visualization of biological networks does typically not apply state-of-the-art graph drawing techniques, and graph drawing tools do not respect the drawing conventions of the life science community. In this paper, we analyze some of the major problems arising in biological network visualization. We characterize these problems and formulate a series of open graph drawing problems. These use cases illustrate the need for efficient algorithms to present, explore, evaluate, and compare biological network data. For each use case, problems are discussed and possible solutions suggested
Drawing Planar 3-Trees with Given Face-Areas
No full textWe study straight-line drawings of planar graphs such that each interior face has a prescribed area. It was known that such drawings exist for all planar graphs with maximum degree 3. We show here that such drawings exist for all planar partial 3-trees, i.e., subgraphs of a triangulated planar graph obtained by repeatedly inserting a vertex in one triangle and connecting it to all vertices of the triangle. Moreover, vertices have rational coordinates if the face-areas are rational, and we can bound the resolution. We also give some negative results for other graph classes
On Planar Supports for Hypergraphs
No full textA graph G is a support for a hypergraph H = (V, S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar. Johnson and Pollak [9] proved that it is NP-complete to decide if a given hypergraph has a planar support. In contrast, there are polynomial time algorithms to test whether a given hypergraph has a planar support that is a path, cycle, or tree. In this paper we present an algorithm which tests in polynomial time if a given hypergraph has a planar support that is a tree where the maximal degree of each vertex is bounded. Our algorithm is constructive and computes a support if it exists. Furthermore, we prove that it is already NP-hard to decide if a hypergraph has a 3-outerplanar support