Compact Hierarchical Graph Drawings via Quadratic Layer Assignment

We propose a new mixed-integer programming formulation that very naturally expresses the layout restrictions of a layered (hierarchical) graph drawing and several associated objectives, such as a minimum total arc length, number of reversed arcs, and width, or the adaptation to a specific drawing area, as a special quadratic assignment problem. Our experiments show that it is competitive to another formulation that we slightly simplify as well

Sugiyama Layouts for Prescribed Drawing Areas

The area of graph drawing is concerned with positioning the elements of a graph on a canvas such that the resulting drawing is well-readable by humans and aids their execution of certain tasks. While known methods are usually well-studied from a theoretical perspective, both their applicability to graphs from practice and their integration into tools from practice are not always satisfactory. This is due to various reasons, for instance, due to known methods usually solving well-defined, self-contained problems that do not cover all of the bits and pieces that must be considered in practice. There, the diagrams the graphs originate from often comprise more than just simple nodes and simple edges, they tend to be messy and complex, and existing methods regularly compute drawings with poor compactness. This thesis is concerned with improving the well-known layer-based layout approach, originally proposed by Sugiyama et al., and devotes special attention to the requirements of dataflow diagrams. It presents new methods for the approach's layer assignment and coordinate assignment steps, and it identifies and illustrates research tasks that are essential to further better the situation in practice