Weak Kernels

摘要

In this paper, we formalize a folklore concept and formally define {em weak kernels} for fixed-parameter computation. We show that a problem has a (traditional) kernel then it also has a weak kernel. It is unknown yet whether the converse is always true. On the other hand, for a problem in NP, if it has a weak kernel then it admits an FPT algorithm (hence a kernel). We show a few applications of weak kernels, for which a (traditional) kernelization seems hard to apply. Among them, we present the first FPT algorithm for the famous Sorting by Minimum Unsigned Reversals problem.