Cologne Excellence Cluster on Cellular Stress Responses in Aging Associated Diseases
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Application of Graph Layout Algorithms for the Visualisation of Biological Networks in 3D
No full textDisconnectivity and Relative Positions in Simultaneous Embeddings
No full textFor two planar graph = (, ) and = (, ) sharing a common subgraph G = ∩ the problem Simultaneous Embedding with Fixed Edges (SEFE) asks whether they admit planar drawings such that the common graph is drawn the same. Previous algorithms only work for cases where G is connected, and hence do not need to handle relative positions of connected components. We consider the problem where G, and are not necessarily connected.
First, we show that a general instance of SEFE can be reduced in linear time to an equivalent instance where = and and are connected. Second, for the case where G consists of disjoint cycles, we introduce the CC-tree which represents all embeddings of G that extend to planar embeddings of . We show that CC-trees can be computed in linear time, and that their intersection is again a CC-tree. This yields a linear-time algorithm for SEFE if all k input graphs (possibly k>2) pairwise share the same set of disjoint cycles. These results, including the CC-tree, extend to the case where G consists of arbitrary connected components, each with a fixed embedding. Then the running time is O(n^2)
Shrinking the Search Space for Clustered Planarity
No full textA clustered graph is a graph augmented with a hierarchical inclusion structure over its vertices, and arises very naturally in multiple application areas. While it is long known that planarity—i.e., drawability without edge crossings—of graphs can be tested in polynomial (linear) time, the complexity for the clustered case is still unknown.
In this paper, we present a new graph theoretic reduction which allows us to considerably shrink the combinatorial search space, which is of benefit for all enumeration-type algorithms. Based thereon, we give new classes of polynomially testable graphs and a practically efficient exact planarity test for general clustered graphs based on an integer linear program
Open Rectangle-of-Influence Drawings of Non-triangulated Planar Graphs
No full textA straight line drawing of a graph is an open weak rectangle-of-influence (RI) drawing if there is no vertex in the relative interior of the axis parallel rectangle induced by the end points of each edge. Despite recent interest of the graph drawing community in rectangle-of-influence drawings, no algorithm is known to test whether a graph has a planar open weak RI-drawing.
In a recent paper, we showed how to test, for inner-triangulated planar graphs, whether they have a planar open weak RI-drawing with a non-aligned frame, i.e., the graph obtained from removing the interior of every filled triangle is drawn such that no two vertices have the same coordinate. In this paper, we generalize this to all planar graphs with a fixed planar embedding, even if some interior faces are not triangles. On the other hand, we show that if the planar embedding is not fixed, then deciding if a given planar graph has an open weak RI-drawing is NP-complete. NP-completeness holds even for open weak RI-drawings with non-aligned frames
Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants
No full textWe study Hanani-Tutte style theorems for various notions of planarity, including partially embedded planarity, and simultaneous planarity. This approach brings together the combinatorial, computational and algebraic aspects of planarity notions and may serve as a uniform foundation for planarity, as suggested in the writings of Tutte and Wu
DAGView: An Approach for Visualizing Large Graphs
No full textIn this paper, we propose a novel visualization framework called DAGView. The aim of DAGView is to produce clear visualizations of directed acyclic graphs in which every edge and the potential existence of a path can be immediately spotted by the user. Several criteria that users identified as important in a layout are met, such as underlying grid, crossings and bends that appear perpendicular. The main algorithm is based on the layout of directed acyclic graphs but can be extended to handle directed graphs with cycles and undirected graphs, taking into account user preferences and/or constraints. Important tasks that are used in user studies are performed efficiently within the DAGView framework
Graph Drawing in TikZ
No full textAt the heart of every good graph drawing algorithm lies an efficient procedure for assigning canvas positions to a graph’s nodes and the bend points of its edges. However, every real-world implementation of such an algorithm must address numerous problems that have little to do with the actual algorithm, like handling input and output formats, formatting node texts, and styling nodes and edges. We present a new framework, implemented in the Lua programming language and integrated into the TikZ graphics description language, that aims at simplifying the implementation of graph drawing algorithms. Implementers using the framework can focus on the core algorithmic ideas and will automatically profit from the framework’s pre- and post-processing steps as well as from the extensive capabilities of the TikZ graphics language and the \TeX typesetting engine. Algorithms already implemented using the framework include the Reingold-Tilford tree drawing algorithm, a modular version of Sugiyama’s layered algorithm, and several force-based multilevel algorithms
Weak Dominance Drawings for Directed Acyclic Graphs
No full textThe dominance drawing method has many important aesthetic properties, including small number of bends, good vertex placement, and symmetry display [1]. Furthermore, it encapsulates the aspect of characterizing the transitive closure of the digraph by means of a geometric dominance relation among the vertices. A dominance drawing Γ of a planar st-graph G is a drawing, such that for any two vertices u and v there is a directed path from u to v in G if and only if and in Γ [1]. Here we study weak dominance drawings where for any two vertices u and v if there is a directed path from u to v in G then and in Γ
Theory and Practice of Graph Drawing
No full textA workshop on Theory and Practice of Graph Drawing was held in conjunction with the International Symposium on Graph Drawing to celebrate Peter Eades's birthday. The workshop was hosted by Microsoft Research in Redmond, Washington, USA, on September 18, 2012. This report reviews the contents of the workshop
Straight Line Triangle Representations
No full textA straight line triangle representation (SLTR) of a planar graph is a straight line drawing such that all the faces including the outer face have triangular shape. Such a drawing can be viewed as a tiling of a triangle using triangles with the input graph as skeletal structure. In this paper we present a characterization of graphs that have an SLTR that is based on flat angle assignments, i.e., selections of angles of the graph that have size π in the representation. We also provide a second characterization in terms of contact systems of pseudosegments. With the aid of discrete harmonic functions we show that contact systems of pseudosegments that respect certain conditions are stretchable. The stretching procedure is then used to get straight line triangle representations. Since the discrete harmonic function approach is quite flexible it allows further applications, we mention some of them.
The drawback of the characterization of SLTRs is that we are not able to effectively check whether a given graph admits a flat angle assignment that fulfills the conditions. Hence it is still open to decide whether the recognition of graphs that admit straight line triangle representation is polynomially tractable