Acknowledgments First of all I want to thank my advisor Petra Mutzel and her group at the department of Algorithms and Data Structures at the Technical University of Vienna for the possibility to write my thesis about this interesting topic and for the outstanding support during the last years. Her great experience and expert knowledge in the field of Graph Drawing was a great help and her enthusiasm for this topic was always a great motivation. This work originated from ideas developed by her group and a number of contributing people and the results could never have been achieved without her support. My special thanks also belong to Gunnar Klau and René Weisskircher. In addition to this thesis they provided me with a number of interesting topics for practical classes and their courses have always been interesting and instructive. Especially I want to thank Gunnar, who took upon him to proofread this thesis and some other papers, and for the large number of fruitful discussions. The major part of the practical work of this thesis was done during a six month stay at the University of La Laguna in Tenerife. I want to thank Prof. Dr. María Belén Melián Batista and her group at the institute for Estadística, Investigación Operativa y Computación for providing me with the necessary facilities, their support and for the possibility to spend a great time on this wonderful island. Furthermore I want to thank Christoph Buchheim, who provided me with a proof-of-concept implementation of our algorithm and for his large number of useful suggestions and ideas. Thanks also to Prof. Barth for representing Prof. Mutzel and to Prof. Raidl and Prof. Krall for holding the final exam. Last but not least I want to thank all my friends for the wonderful time we spent together and my parents for their support during all those years. i Short Abstract In this thesis we study the Crossing Minimization Problem. We are looking for a drawing for a given graph in the plane, such that a minimum number of edges cross. Although this problem was shown to be NP hard, algorithms are needed in practice. Application areas occur, e.g., in the area of Graph Drawing and VLSI design. While the problem mostly is attacked using heuristic approaches in practice, we present an algorithm that is able to solve medium sized instances to provable optimality in reasonable computation time. …
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