From the W-hierarchy to XNLP: Classes of Fixed Parameter Intractability

Abstract

In this short survey, a number of old and new notions from parameterized complexity are discussed. We start with looking at the W-hierarchy, including the classes W[1], W[2], W[P]. Then, a recent development where problems are shown to be complete for simultaneously non-deterministic time of the form f(k) nc and space of the form f(k) log n, is discussed. Some consequences and other notions are briefly explored.