In chapters 2-5 of this thesis we give new geometric algorithms to solve four selected GIS problems. These chapters are preceded by an introduction that provides the necessary background, overview, and definitions to appreciate the following chapters. This is the first algorithm that guarantees a seed set of minimum size. Its running time is quadratic in the input size, which is not fast enough for many practical situations. When settlements, such as cities, have to be displayed on a map, displaying all of them may clutter the map, depending on the map scale.
Choices have to be made which settlements are selected, and which ones are omitted.
Compared to existing selection methods, our methods have a number of favorable properties.