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Beschreibung:
This thesis investigates the requirements for graph drawing stemming from practical applications, and presents both theoretical as well as practical results and approaches to handle them. Many approaches to compute graph layouts in various drawing styles exist, but the results are often not sufficient for use in practice. Drawing conventions, graphical notation standards, and user-defined requirements restrict the set of admissible drawings. These restrictions can be formalized as constraints for the layout computation. We investigate the requirements and give an overview and categorization of the corresponding constraints. Of main importance for the readability of a graph drawing is the number of edge crossings. In case the graph is planar it should be drawn without crossings, otherwise we should aim to use the minimum number of crossings possible. However, several types of constraints may impose restrictions on the way the graph can be embedded in the plane. These restrictions may have a strong impact on crossing minimization. For two types of such constraints we present specific solutions how to consider them in layout computation: We introduce the class of so-called embedding constraints, which restrict the order of the edges around a vertex. For embedding constraints we describe approaches for planarity testing, embedding, and edge insertion with the minimum number of crossings. These problems can be solved in linear time with our approaches. The second constraint type that we tackle are clusters. Clusters describe a hierarchical grouping of the graph's vertices that has to be reflected in the drawing. The complexity of the corresponding clustered planarity testing problem for clustered graphs is unknown so far. We describe a technique to compute a maximum clustered planar subgraph of a clustered graph. Our solution is based on an Integer Linear Program (ILP) formulation and includes also the first practical clustered planarity test for general clustered graphs. The resulting subgraph can be used within the ...