New races in parameterized algorithmics

Abstract

Once having classified an NP-hard problem fixed-parameter tractable with respect to a certain parameter, the race for the most efficient fixed-parameter algorithm starts. Herein, the attention usually focuses on improving the running time factor exponential in the considered parameter, and, in case of kernelization algorithms, to improve the bound on the kernel size. Both from a practical as well as a theoretical point of view, however, there are further aspects of efficiency that deserve attention. We discuss several of these aspects and particularly focus on the search for "stronger parameterizations" in developing fixed-parameter algorithms. © 2012 Springer-Verlag.