Abstract
This thesis aims for the development of efficient algorithms to exactly solve four selected NPhard graph and hypergraph problems arising in the fields of scheduling, steel manufacturing, software engineering, radio frequency allocation, computer-aided circuit design, and social network analysis. NP-hard problems presumably cannot be solved exactly in a running time growing only po lynomially with the input size. In order to still solve the considered problems efficiently, this thesis develops linear-time data reduction and fixed-parameter linear-time algorithms—algorithms that can be proven to run in linear time if certain parameters of the problem instances are constant. Besides proving linear worst-case running times, the efficiency of most of the developed algorithms is evaluated experimentally. Moreover, the limits of fixed-parameter linear-time algorithms and provably efficient and effective data reduction are shown.
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