Graphs are a frequently used tool to model relationships among entities. A graph is a binary relation between objects, that is, it consists of a set of objects (vertices) and a set of pairs of objects (edges). Networks are common examples of modeling data as a graph. For example, relationships between persons in a social network, or network links between computers in a telecommunication network can be represented by a graph. The clearest way to illustrate the modeled data is to visualize the graphs. The field of Graph Drawing deals with the problem of finding algorithms to automatically generate graph visualizations. The task is to find a "good" drawing, which can be measured by different criteria such as number of crossings between edges or the used area. In this thesis, we study Angular Schematization in Graph Drawing. By this, we mean drawings with large angles (for example, between the edges at common vertices or at crossing points). The thesis consists of three parts. First, we deal with the placement of boxes. Boxes are axis-parallel rectangles that can, for example, contain text. They can be placed on a map to label important sites, or can be used to describe semantic relationships between words in a word network. In the second part of the thesis, we consider graph drawings visually guide the viewer. These drawings generally induce large angles between edges that meet at a vertex. Furthermore, the edges are drawn crossing-free and in a way that makes them easy to follow for the human eye. The third and final part is devoted to crossings with large angles. In drawings with crossings, it is important to have large angles between edges at their crossing point, preferably right angles.

The general map-labeling problem is as follows: given a set of geometric objects to be labeled, or features, in the plane, and for each feature a set of label positions, maximize the number of placed labels such that there is at most one label per feature and no two labels overlap. There are three types of features in a map: point, line, and area features. Unfortunately, one cannot expect to find efficient algorithms that solve the labeling problem optimally. Interactive maps are digital maps that only show a small part of the entire map whereas the user can manipulate the shown part, the view, by continuously panning, zooming, rotating, and tilting (that is, changing the perspective between a top and a bird view). An example for the application of interactive maps is in navigational devices. Interactive maps are challenging in that the labeling must be updated whenever labels leave the view and, while zooming, the label size must be constant on the screen (which either makes space for further labels or makes labels overlap when zooming in or out, respectively). These updates must be computed in real time, that is, the computation must be so fast that the user does not notice that we spend time on the computation. Additionally, labels must not jump or flicker, that is, labels must not suddenly change their positions or, while zooming out, a vanished label must not appear again. In this thesis, we present efficient algorithms that dynamically label point and line features in interactive maps. We try to label as many features as possible while we prohibit labels that overlap, jump, and flicker. We have implemented all our approaches and tested them on real-world data. We conclude that our algorithms are indeed real-time capable.

Maps are the main tool to represent geographical information. Users often zoom in and out to access maps at different scales. Continuous map generalization tries to make the changes between different scales smooth, which is essential to provide users with comfortable zooming experience. In order to achieve continuous map generalization with high quality, we optimize some important aspects of maps. In this book, we have used optimization in the generalization of land-cover areas, administrative boundaries, buildings, and coastlines. According to our experiments, continuous map generalization indeed benefits from optimization.

Constraining graph layouts - that is, restricting the placement of vertices and the routing of edges to obey certain constraints - is common practice in graph drawing. In this book, we discuss algorithmic results on two different restriction types: placing vertices on the outer face and on the integer grid. For the first type, we look into the outer k-planar and outer k-quasi-planar graphs, as well as giving a linear-time algorithm to recognize full and closed outer k-planar graphs Monadic Second-order Logic. For the second type, we consider the problem of transferring a given planar drawing onto the integer grid while perserving the original drawings topology; we also generalize a variant of Cauchy's rigidity theorem for orthogonal polyhedra of genus 0 to those of arbitrary genus.