Abstract:
Polynomial-time preprocessing is a simple algorithmic strategy which has been
widely employed in practice to tackle hard problems. The quantification and
analysis of the efficiency of preprocessing algorithms are, in a certain precise
sense, outside the pale of classical complexity theory. The notion of kernelization from parameterized complexity theory provides a framework for the mathematical analysis of polynomial-time preprocessing algorithms. Both kernelization and the closely related notion of fixed-parameter tractable (FPT) algorithms are very active areas of current research. In this thesis we describe the results of our study of the kernelization complexity of some graph domination and covering problems.
