Zyklische Levelzeichnungen gerichteter Graphen

The Sugiyama framework proposed in the seminal paper of 1981 is one of the most important algorithms in graph drawing and is widely used for visualizing directed graphs. In its common version, it draws graphs hierarchically and, hence, maps the topological direction to a geometric direction. However, such a hierarchical layout is not possible if the graph contains cycles, which have to be destroyed in a preceding step. In certain application and problem settings, e.g., bio sciences or periodic scheduling problems, it is important that the cyclic structure of the input graph is preserved and clearly visible in drawings. Sugiyama et al. also suggested apart from the nowadays standard horizontal algorithm a cyclic version they called recurrent hierarchies. However, this cyclic drawing style has not received much attention since. In this thesis we consider such cyclic drawings and investigate the Sugiyama framework for this new scenario. As our goal is to visualize cycles directly, the first phase of the Sugiyama framework, which is concerned with removing such cycles, can be neglected. The cyclic structure of the graph leads to new problems in the remaining phases, however, for which solutions are proposed in this thesis. The aim is a complete adaption of the Sugiyama framework for cyclic drawings. To complement our adaption of the Sugiyama framework, we also treat the problem of cyclic level planarity and present a linear time cyclic level planarity testing and embedding algorithm for strongly connected graphs

Two-Layer Planarization in Graph Drawing

We study the two-layer planarization problems that have applications in Automatic Graph Drawing. We are searching for a two-layer planar subgraph of maximum weight in a given two-layer graph. Depending on the number of layers in which the vertices can be permuted freely, that is, zero, one or two, different versions of the problems arise. The latter problem was already investigated in [11] using polyhedral combinatorics. Here, we stud

Two-Layer Planarization in Graph Drawing

. We study the two-layer planarization problems that have applications in Automatic Graph Drawing. We are searching for a two-layer planar subgraph of maximum weight in a given two-layer graph. Depending on the number of layers in which the vertices can be permuted freely, that is, zero, one or two, different versions of the problems arise. The latter problem was already investigated in [11] using polyhedral combinatorics. Here, we study the remaining two cases and the relationships between the associated polytopes. In particular, we investigate the polytope P1 associated with the twolayer planarization problem with one fixed layer. We provide an overview on the relationships between P1 and the polytope Q1 associated with the two-layer crossing minimization problem with one fixed layer, the linear ordering polytope, the two-layer planarization problem with zero and two layers fixed. We will see that all facet-defining inequalities in Q1 are also facet-defining for P1 . Furthermore, w..