Parallel algorithms for rational cones and affine monoids

Acknowledgements First of all I would like to thank my advisor Winfried Bruns for his inspiring guidance and support. Our discussions have been very helpful, and I am always enjoying to work with him. I also wish to thank all my colleagues at the Institute for Mathematics. They are providing a very pleasant working atmosphere. Many thanks also to Merle for listening to my incomprehensible discourses and her standby in various ways. Moreover, I thank all of my friends for offering me advice and distraction, especially Jochen for thought-provoking discussions on algorithms and parallelization. Special thanks to my family. They provided excellent frame conditions for my whole undergraduate and doctoral studies.