Weak Kernels

In this paper, we formalize a folklore concept and formally define weak kernels for fixedparameter 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. Department of Computer Science, Montana State University, Bozeman, MT 59717, USA. Email: [email protected]. Corresponding author. Department of Computer Science, Montana State University, Bozeman, MT 59717, USA. Email: [email protected].