Lehrinhalte
Many algorithmic problems on graphs are NP-hard and therefore there is good evidence that no efficient algorithms solving these problems on all graphs exist. Classical examples are routing problems arising e.g. in integrated circuit layout and
design, colouring problems in scheduling applications or domination problems in facility location.
However, instances to these problems arising in practical applications may have more ”structure“ than general graphs, e.g. instances may be “hierarchical” or “tree-like”. Using this additional structural information may help in designing efficient
algorithms for solving problems in instances of this form.
A particularly good example are instances which are planar graphs, i.e. graphs that can be drawn without crossing edges. Planar graphs arise for instance in routing applications, as many road or train maps are nearly planar. It turns out that if the input instance is planar, or a tree, then many hard problems become tractable.
In this course we will study methods for solving algorithmic problems on restricted classes of graphs. The most important cases will be planar graphs and graph classes defined by the concept of bounded tree-width. We will then extend this to even more general classes of graphs.
The focus of this lecture is to introduce the structural properties of graphs that can be employed in the design of efficient algorithms and to present the algorithmic techniques needed for this.
