Algorithms for dynamic geometric data streams

Acknowledgements First of all I would like to thank my advisor Christian Sohler for his great support. It was not always easy to keep pace with his great ability to find interesting problems and develop new ideas to solve them. During the whole time he gave me the feeling that I can always ask (even stupid) questions and was responsible for the great atmosphere in Paderborn. Without the fun I had at work I would have never been able to develop the results presented in this thesis. I also benefited a lot from the great experience of my co-advisor Friedhelm Meyer auf der Heide. He gave me the opportunity to come to Paderborn and the freedom to choose a research area to work on. He always lent a sympathetic ear for all kinds of problems. I would also like to thank Friedhelm's whole research group for the nice time in Paderborn. Then I would like to thank Kristina for her patience, empathy, love, and all the other things that make it so worthwhile to know her. She turned even the most stressful days into a wonderful time. Finally I would like to thank those whom I owe the most: my parents, Adolf and Margret. They always gave me the feeling to be loved and supported, whatever I am going to do in my life.